Karman

W. Tubes, turbulent, smooth tubes. Constant surface concentration. Von Karman analogy... 

Blade stall causes Karman vortices in the airfoil wake. Whenever the frequency of these vortices coincides with the natural frequency of the airfoil, flutter will occur. Stall flutter is a major cause of compressor blade failure. 

The Born-von Karman boundary conditions then restrict the allowed electronic states to those in the graphene Brillouin zone that satisfy... 

Skiiret, E. 1993. Advanced design of ventilation systems Ventilation models. Lecture Series, Von Karman Institute for Fluid Dynamics. 

E. Skiiret, Advanced Design of Ventilation System, Ventilation Models Lecture Series, Brussels Von Karman Institute for Fluid Dvnamics, 1993. 

The Reynolds number, which is directly proportional to the air velocity and the size of the obstacle, is a critical quantity. According to photographs presented elsewhere, a regular Karman vortex street in the wake ot a cylinder is observed only in the range of Reynolds numbers from about 60 to 5000. At lower Reynolds numbers, the wake is laminar, and at higher Reynolds numbers, there is a complete turbulent mixing. 

However, one should be cautious when comparing the Reynolds number from regular Karman vortex streets with the Reynolds number calculated from factual situations in clean benches as the airflow from behind an obstacle is usually not the typically formed Karman vortex street predicted for an indefinitely long circular cylinder. The wake situations during actual conditions often seem to have a three-dimensional stmcnire. 

Timmermans, A.R.J. (1978), Combined Cycles and Their Possibilities. In Von Karman Institute for Fluid Dynamics, Lecture Series 6, Vol. 1. 

Available from Wavefunction, Inc., 18401 Von Karman Avenue, Suite 370, Irvine, CA 92612. 

Hasson, D., Karman, M., 5th. International Conference on the Internal and External Protection of Pipes, Innsbruck, Austria, conference sponsored by BHRA, Cranfield, England (October 1983)... 

Meanwhile, the flow near the cylinder curls towards the cylinder and forms a new vortex that takes the place of the original. As time goes on, the vortices on either side of the cylinder take turns breaking off and traveling down stream. A snapshot of this behavior is shown schematically in figure 9.3. This stream of successively broken-off vortices is known as a von Karman vortex street [trittSS]. 

A little bit of physical intuition as to how the vortices form in the first place may help in explaining the behavior as TZ is increased still further. We know that u = 0 at the cylinder s surface. We also know that the velocity increases rapidly as we get further from that surface. Therefore vortices are due to this rapid local velocity variation. If the variation is small enough, there is enough time for the vorticity to diffuse out of the region just outside the cylinder s surface and create a large von Karman vortex street of vorticity down stream [feyn64]. 

When a bluff body is interspersed in a fluid stream, the flow is split into two parts. The boundary layer (see Chapter 11) which forms over the surface of the obstruction develops instabilities and vortices are formed and then shed successively from alternate sides of the body, giving rise to what is known as a von Karman vortex street. This process sets up regular pressure variations downstream from the obstruction whose frequency is proportional to the fluid velocity, as shown by Strouai. 9. Vortex flowmeters are very versatile and can be used with almost any fluid — gases, liquids and multi-phase fluids. The operation of the vortex meter, illustrated in Figure 6.27, is described in more detail in Volume 3, by Gjnesi(8) and in a publication by a commercial manufacturer, Endress and Hauser.10 ... 

Note that the Kolmogorov power spectrum is unphysical at low frequencies— the variance is infinite at k = 0. In fact the turbulence is only homogeneous within a finite range—the inertial subrange. The modified von Karman spectral model includes effects of finite inner and outer scales. 

Figure 1. Kolmogorov and modified von Karman spectral models. (Lo = 10 m and o 0.01 m for the von Karman plot.)...

Nonpremixed edge flames (a) 2D mixing layer (From Kioni, P.N., Rogg, B., Bray, K.N.C., and Linan, A., Combust. Flame, 95, 276, 1993. With permission.), (b) laminar jet (From Chung, S.H. and Lee, B.J., Combust. Flame, 86, 62,1991.), (c) flame spread (From Miller, F.J., Easton, J.W., Marchese, A.J., and Ross, H.D., Proc. Combust. Inst., 29, 2561, 2002. With permission.), (d) autoignition front (From Vervisch, L. and Poinsot, T., Annu. Rev. Fluid Mech., 30, 655, 1998. With permission.), and (e) spiral flame in von Karman swirling flow (From Nayagam, V. and Williams, F.A., Combust. Sci. Tech., 176, 2125, 2004. With permission.). (LPF lean premixed flame, RPF rich premixed flame, DF diffusion flame). 

Similarity solutions of the velocity profile functions for the Von Karman problem. (From Von Karman, Th, Z., Angew. Math. Mech., 1,231,1921.)... 

Von Karman, Th.,Uber laminare und turbulente Reibung, Zeitschrift fur Angewandte Mathematik und Mechanik, 1, 231-251, 1921. 

Zandbergen, RJ. and Dijkstro, D., Von Karman swirling flows. Annual Review of Fluid Mechanics., 19,465M91,1981. 

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