Correlation of data on the statistical theory of turbulence

The statistical theory of turbulence affords an excellent medium for representing the kinematic conditions in turbulent flow and also serves as a valuable aid to exact experimental research. But it is still not developed enough for solving dynamic processes. Even in the simplest case of isotropic turbulence the calculation of the correlation curve or of the decrement of turbulence invariably reaches a point where clear-cut assumptions, such as omission of the inertia terms, or, earlier, mixing length assumptions or even merely general dimensional considerations, must be made

Zur Strukturchemie der Diperoxovanadate(V): Das μ-Hydroxo-bis [oxo-diperoxovanadat(V)] Anion

Depending on the pH and the respective concentrations of solutions containing NH4+/NH3/H2O2/NH4VO3 three yellow ammonium salts can be isolated: (NH4)4[O(VO(O2)2)2], NH4[VO(O2)2NH3]; and the novel (NH4)3[HV2O11] · 2 H2O. A cesium and potassium salt of the latter anion have been prepared. The infrared spectra of these salts are interpreted assuming a μ-hydroxo-bis[oxo-diperoxovanadate(V)] structure in the solid state

On the turbulent friction layer for rising pressure

Among the information presented are included displacement, momentum, and kinetic energy thicknesses, shearing stress distributions across boundary layer, and surface friction coefficients. The Gruschwitz method and its modifications are examined and tested. An energy theorem for the turbulent boundary layer is introduced and discussed but does not lead to a method for the prediction of the behavior of the turbulent boundary layer because relations for the shearing stress and the surface friction are lacking

Pressure and Motion of Dry Sand -- Translation of Hagen's Paper from 1852

In a remarkable paper from 1852, Gotthilf Heinrich Ludwig Hagen measured and explained two fundamental aspects of granular matter: The first effect is the saturation of pressure with depth in a static granular system confined by silo walls -- generally known as the Janssen effect. The second part of his paper describes the dynamics observed during the flow out of the container -- today often called the Beverloo law -- and forms the foundation of the hourglass theory. The following is a translation of the original German paper from 1852.Comment: 4 pages, accepted for publication in Granular Matter, original article (German) can be found under http://www.phy.duke.edu/~msperl/Janssen

Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward to implement in three dimensions. Furthermore, especially for parallelized solvers it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it is capable to accurately model the velocity field up to second order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio

Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular Nanomagnet

The spin-lattice relaxation rate $T_{1}^{-1}$ and NMR spectra of $^1$H in single crystal molecular magnets of Fe8 have been measured down to 15 mK. The relaxation rate $T_1^{-1}$ shows a strong temperature dependence down to 400 mK. The relaxation is well explained in terms of the thermal transition of the iron state between the discreet energy levels of the total spin S=10. The relaxation time $T_1$ becomes temperature independent below 300 mK and is longer than 100 s. In this temperature region stepwise recovery of the $^1$H-NMR signal after saturation was observed depending on the return field of the sweep field. This phenomenon is attributed to resonant quantum tunneling at the fields where levels cross and is discussed in terms of the Landau-Zener transition.Comment: 13 pages, 5 figure

Anomalous density dependence of static friction in sand

We measured experimentally the static friction force $F_s$ on the surface of a glass rod immersed in dry sand. We observed that $F_s$ is extremely sensitive to the closeness of packing of grains. A linear increase of the grain-density yields to an exponentially increasing friction force. We also report on a novel periodicity of $F_s$ during gradual pulling out of the rod. Our observations demonstrate the central role of grain bridges and arches in the macroscopic properties of granular packings.Comment: plain tex, 6 pages, to appear in Phys.Rev.

Recalibration of the Shear Stress Transport Model to Improve Calculation of Shock Separated Flows

The Menter Shear Stress Transport (SST) k . turbulence model is one of the most widely used two-equation Reynolds-averaged Navier-Stokes turbulence models for aerodynamic analyses. The model extends Menter s baseline (BSL) model to include a limiter that prevents the calculated turbulent shear stress from exceeding a prescribed fraction of the turbulent kinetic energy via a proportionality constant, a1, set to 0.31. Compared to other turbulence models, the SST model yields superior predictions of mild adverse pressure gradient flows including those with small separations. In shock - boundary layer interaction regions, the SST model produces separations that are too large while the BSL model is on the other extreme, predicting separations that are too small. In this paper, changing a1 to a value near 0.355 is shown to significantly improve predictions of shock separated flows. Several cases are examined computationally and experimental data is also considered to justify raising the value of a1 used for shock separated flows

Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations

During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not implemented. These include for example multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results by applying the algorithm to a Fontainebleau sandstone and by comparing our benchmark studies to other numerical permeability measurements in the literature.Comment: 14 pages, 11 figure