Von Karman

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

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. 

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. 

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. 

Here V is the volume of the Bom-von Karman region, i.e. that part of position space which is repeated as a result of the fundamental periodic boundary conditions. The integration in (11.1) is carried out over that region, which we denote by BK. 

As developed by Dukler, Deissler s expression for e was used for the region near the wall, and, von Karman s relationship was used for highly developed turbulent flow. 

Cheremisinoff and Davis (1979) relaxed these two assumptions by using a correlation developed by Cohen and Hanratty (1968) for the interfacial shear stress, using von Karman s and Deissler s eddy viscosity expressions for solving the liquid-phase momentum equations while still using the hydraulic diameter concept for the gas phase. They assumed, however, that the velocity profile is a function only of the radius, r, or the normal distance from the wall, y, and that the shear stress is constant, t = tw. ... 

For the liquid phase, Cheremisinoff and Davis (1979) solved the momentum equation using von Karman s and Deissler s eddy viscosity expressions. 

This equation is called the von Karman equation (or, sometimes, the law of the wall ), and can be written in the following dimensionless form... 

Equation (6-35) is also known as the von Karman-Nikuradse equation and agrees well with observations for friction loss in smooth pipe over the range 5 x 103 < NRe < 5 x 106. 

Equation (6-37) represents the friction factor for Newtonian fluids in smooth tubes quite well over a range of Reynolds numbers from about 5000 to 105. The Prandtl mixing length theory and the von Karman and Blasius equations are referred to as semiempirical models. That is, even though these models result from a process of logical reasoning, the results cannot be deduced solely from first principles, because they require the introduction of certain parameters that can be evaluated only experimentally. 

---