Catálogo de publicaciones - libros

The understanding of the complex statistics of fully developed turbulence in detail is still an open problem. One of the central points is to understand intermittency, i.e. to find exceptionally strong fluctuations on small scales. In the last years, the intermittency in different directions has attracted considerable interest. It has been controversial whether there are significant differences in intermittency between the different directions. More specifically one looks at the statistics of increments [( + ) − ()] , i.e. at the projection of the differences between two velocities separated by the vector in a certain direction . Here we denotes longitudinal increments with , for which and are parallel and transverse increments with for which is perpendicular to .

In a first step, one commonly investigates the statistics with the moments of the increments, the so-called structure functions, and assumes that, according to Kolmogorov, the structure functions obey a scaling law <> ∝ at least for sufficient high Reynolds number. The intermittency problem is then expressed by the deviation of the exponent ξ from the value /3, the well-known Kolmogorov (1941) scaling.

A conditional moment closure approach for modelling turbulent combustion is proposed, based on two conditioning variables. The two conditioning variables used here are mixture fraction and a second conserved scalar , which is initialized perpendicular to the mixture fraction, such that the two conditioning variables constitute a plane. With this we hope to capture important physical features of turbulent reacting flows which the single conditioning variable approach cannot, including local ignition, extinction and re-ignition due to small scale strain fluctuations. We propose to model the stress tensor with a stochastic process to account for chaotic turbulent fluctuations.

Probability density functions (PDF) present seducing features for modelling turbulent reactive flows: they carry a detailed one-point statistical information and allow to treat chemical source terms exactly. But to be able to take full advantage of those modelling abilities, it is first necessary to possess an efficient numerical method to solve PDF equations.

In this article, this issue is adressed in the frame of Eulerian Monte Carlo methods: stochastic partial differential equations which are stochastically equivalent to the PDF equations are proposed and applied to the calculation of the PDF of a reactive scalar.

A rigorous asymptotic analysis concerning the phenomenon of non-uniqueness of quasi-equilibrium turbulent boundary layers in the large Reynolds number limit has recently been carried out in [2]. The approach contains the classical asymptotic theory of wall-bounded turbulent shear flows, cf. [3], as a limiting case. Compared to the latter, the novel theory allows for a moderately large but still asymptotically small velocity defect with respect to the external inviscid flow. Therefore, it applies to attached flow only which, however, exhibits some properties known from separating turbulent boundary layers. Here a first comparison of the theoretical results with numerical and experimental data is presented. As a special aspect, the impact of the equilibrium conditions on the associated external potential flow field is elucidated.

The measurements were performed in the 8 × 6 test section of the low-speed German-Dutch wind tunnel (DNW-LLF) at Reynolds numbers up to = 50 × 10 in a zero pressure gradient turbulent boundary layer with a maximum thickness of 150 mm. Two triple hot-wire probes were used, one of which could be shifted in the vertical direction and the other one could be moved such that geometrically a three-dimensional wedge-like zone above the surface of the flat plate could be analyzed. Furthermore, 2C and 3C Particle-Image Velocimetry (PIV) measurements were done to obtain the instantaneous flow structure in a complete plane and to check the validity of fundamental assumptions such as the Taylor hypothesis.

In this chapter, we make an inventory of the tools suitable for supporting exploratory data analysis. Our major point is that the primary tool for analysis is the human imaginative mind, and that all other tools are supplementary. Only the human mind actually does the analysis; the other tools supply it with the necessary material, appropriately prepared and presented. The most appropriate form for the presentation of such material is visual, since the mind, as most scientists tend to agree, operates predominantly with images.

The techniques and software tools usable in exploratory data analysis are currently very numerous, and new tools continue to appear. It would be completely unfeasible to survey all of them. Therefore, we have tried instead to set out the major tool categories and describe the key functions and properties of each category. The resulting classification looks as follows:

We divide the visual expressive means into display dimensions and visual, or retinal, variables. Display dimensions provide a set of positions within a display at which graphical elements, or marks, can be placed. Retinal variables represent various properties of the marks: shape, size, colour, texture, orientation, etc. In addition to the visual dimensions of a display, such as width, height, or depth, we consider also the display time, which can be used, for example, in animated presentations.

In exploratory data analysis, it is usually not enough to use a single tool. Various tools need to be combined. We consider two basic modes of tool combination, sequential and concurrent, and discuss the various mechanisms used for tool combination. Visualisation is an essential component of any tool ensemble. Initial data visualisation is used in order to understand what tools should be used for further work. Results produced by any non-visual tool need to be visualised so that the analyst can see and interpret them

Throughout this chapter, we provide many examples of various tools. Even when discussing non-visual tools such as data manipulation or computational methods, we use visualisation intensively to illustrate the examples. Readers can easily note that we have taken every opportunity to stress the great role of visualisation in exploratory data analysis. At the beginning of the chapter, we make an attempt to substantiate the importance of visualisation.

Lie group analysis is used to derive (exponential laws) for ZPG turbulent boundary layer flow. A new scaling group was found in the two-point correlation equations. DNS of such a flow was performed at = 2240 using a spectral method with up to 160 million grid points. The results of the numerical simulations are compared with the new scaling laws and good agreement is achieved.

Based on Patent application DE 198 22 125.8-52, we present a technical description of a new temporal and spatial high resolving anemometer for gas and liquid flows. The measurement principle is based on the technique of an atomic force microscope where microstructured cantilevers are used to detect extreme small forces. We show the sensor as a small compact unit and present first measurements and characterizations.

Based on Patent application DE 198 22 125.8-52, we present a technical description of a new temporal and spatial high resolving anemometer for gas and liquid flows. The measurement principle is based on the technique of an atomic force microscope where microstructured cantilevers are used to detect extreme small forces. We show the sensor as a small compact unit and present first measurements and characterizations.

Two series of visualization experiments were performed in the boundary layer of Rayleigh—Bénard convection with the goal to get more information on the behavior and characteristics of streaks elongated in the streamwise direction observed in the boundary layers. These streamwise streaks are a new type of coherent structures in the Rayleigh—Bénard convection.