last modified 12/02/2003
Course code: wb1424ATU ECTS credit points: 6 |
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| Faculty of Mechanical Engineering and Marine Technology | |
| Lecturer(s): Westerweel, prof.dr.ir. J. | Tel.: 015-27 86887 |
| Catalog data: Turbulence, Stability theory, Chaos, Turbulence models, Turbelent kinetic Energy, Vorticity, Correlation function, Spectrum, Dispersion |
Course year: MSc
1st year Semester: 2A / 2B Hours p/w: 2 Other hours: -- Assessment: written Assessm. period(s): 2B, August (see academic calendar) |
| Prerequisites: wb1422A | |
| Follow up: wb1424B | |
| Detailed description of topics: In this course an introduction is given in the theory of turbulence. The point of departure is the treatment of linear stability theory applied to Kelvin-Helmholtz instability, the inflection criterion of Rayleigh and the Orr-Sommerfeld equation. Following the results of linear theory new insights in the generation of turbulence are considered, i.e. the routes to chaos. Next follows a phenomenological treatment of turbulence, based on the solution of the Burgers equation. The statistical treament of stochastic processes is discussed and with it the Reynolds equations are derived from the Navier-Stoker equations. This leads to a discussion of the closure problem and the introduction of turbulence modeling. The results are then applied to a one-dimensional channel flow in which we introduce the logarithmic velocity profile. The turbulence energy equation is discussed and we introduce the cascade process. At the same time the one-equation model for turbulence is discussed and the Rotta hypothesis for the exchange of energy between coordinate directions. The next equation to be treated is the vorticity equation and with this equation the role of vorticity stretching in turbulence is discussed. The equation for enstrophy is derived and this leads to a two-equation model of turbulence such as the k-e model. De disadvantages of K-theory are discussed and attention is given to second-order closure models. The next step is to introduce two-points correlations and their Fourier transform: spectra. By means of scaling the 5/3 spectrum in the inertial sub-range is derived. The last topics are isotropic turbulence and dispersion. |
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| Course material: Turbulence by F.T.M. Nieuwstadt, Epsilon Publication No. 24, Utrecht (in Dutch); H. Tennekes and J.L. Lumley, A First Course in Turbulence |
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References from
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| Remarks (specific information
about assessment, entry requirements, etc.): Extra credit for assessment can be gained via homework. |
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| Goals: Introduction into turbulence so that at the end one is able to follow the international scientific literature in this field and to perform research in this area. |
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| Computer use: Computers are used for demonstrations of the lecture material during the course on the basis of commercial software. |
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| Laboratory project(s): During the lecture some demonstrations are carried out to explain and support the course material. |
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| Design content: In this course turbulence models are treated which are used in various design procedures. |
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| Percentage of design: 0% | |