Multidimensional optimization of finite difference schemes for Computational Aeroacoustics

Because of the long propagation distances, Computational Aeroacoustics schemes must propagate the waves at the correct wave speeds and lower the isotropy error as much as possible. The spatial differencing schemes are most frequently analyzed and optimized for one-dimensional test cases. Therefore, in multidimensional problems such optimized schemes may not have isotropic behavior. In this work, optimized finite difference schemes for multidimensional Computational Aeroacoustics are derived which are designed to have improved isotropy compared to existing schemes. The derivation is performed based on both Taylor series expansion and Fourier analysis. Various explicit centered finite difference schemes and the associated boundary stencils have been derived and analyzed. The isotropy corrector factor, a parameter of the schemes, can be determined by minimizing the integrated error between the phase or group velocities on different spatial directions. The order of accuracy of the optimized schemes is the same as that of the classical schemes, the advantage being in reducing the isotropy error. The present schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates. The optimized schemes are tested by solving various multidimensional problems of Aeroacoustics.     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Flow visualization and pressure distributions in a model of the glottis with a symmetric and oblique divergent angle of 10 degrees

Modeling the human larynx can provide insights into the nature of the flow and pressures within the glottis. In this study, the intraglottal pressures and glottal jet flow were studied for a divergent glottis that was symmetric for one case and oblique for another. A Plexiglas model of the larynx (7.5 times life size) with interchangeable vocal folds was used. Each vocal fold had at least 11 pressure taps. The minimal glottal diameter was held constant at 0.04 cm. The glottis had an included divergent angle of 10 degrees. In one case the glottis was symmetric. In the other case, the glottis had an obliquity of 15 degrees. For each geometry, transglottal pressure drops of 3, 5, 10, and 15 cm H2O were used. Pressure distribution results, suggesting significantly different cross-channel pressures at glottal entry for the oblique case, replicate the data in another study by Scherer et al. [J. Acoust. Soc. Am. 109, 1616-1630 (2001b)]. Flow visualization using a LASER sheet and seeded airflow indicated separated flow inside the glottis. Separation points did not appear to change with flow for the symmetric glottis, but for the oblique glottis moved upstream on the divergent glottal wall as flow rate increased. The outgoing glottal jet was skewed off-axis for both the symmetric and oblique cases. The laser sheet showed asymmetric circulating regions in the downstream region. The length of the laminar core of the glottal jet was less than approximately 0.6 cm, and decreased in length as flow increased. The results suggest that the glottal obliquity studied here creates significantly different driving forces on the two sides of the glottis (especially at the entrance to the glottis), and that the skewed glottal jet characteristics need to be taken into consideration for modeling and aeroacoustic purposes.     

On the discontinuous Galerkin computation of N‐waves focusing

Sonic boom focusing phenomenon can be predicted using the solution to the nonlinear Tricomi equation which is a hybrid (hyperbolic‐elliptic) second‐order partial differential equation. In this paper, the hyperbolic conservation law form is derived, which is valid in the entire domain. In this manner, the presence of two regions where the equation behaves differently (hyperbolic in the upper and elliptic in the lower half‐plane) is avoided. On the upper boundary, a new mixed boundary condition for the acoustic pressure is employed. The discretization is carried out using a discontinuous Galerkin (DG) method combined with a Runge–Kutta total‐variation diminishing scheme. The results show the accuracy of DG methods to solve problems involving sharp gradients and discontinuities. Comparisons with analytical results for the linear case, and other numerical results using classical explicit and compact finite difference schemes and weighted essentially non‐oscillatory schemes are included. Copyright © 2010 John Wiley & Sons, Ltd.     

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several mil...     

Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation

The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2μm （diameter） polystyrene. The liquid mixtures, in the proper proportions of water （H2O）, deuterium oxide （D2O） and methanol （MeOH） as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes （reduction） in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary the influence of the sedimentation on coagulation rates at corrections for all factors, our experiments show that the initial stage of the coagulation is not observable.