平板上の亂流限界層に就て
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There are some theories on turbulent flow, such as momentum transfer theory, vorticity transfer theory and similarity theory. I prope here a mean vortex theory, in which the turbulence is considered to be composed of very fine vortices. These vortices decay or grow, but in a very small region their mean strength is not altered, and it is a function of space. The velocity distribution in a turbulent boundary layer is governed by the distribution of mean vortices. The equation of boundary layer on a flat plate is expressed by [numerical formula] (1) This is transformed by introducing the vorticity ζ as follows: [numerical formula]. (2) The first term of this equation means the variation of kinetic energy in the x direction, the second term means the Magnus effect acting on the vortex at a point considered. Starting from these considerations, and considering the mean vortex in an elementary area the following equation is derived, [numerical formula], (3) in which a, b and c are constants and w is the strength of a mean vortex. The general solution of (3) is [numerical formula], (4) u is derived from this equation, remembering w=∂u/∂y. I take two particular cases of (4). The one is expressed by the equation (7) on page 486, from which local friction coefficient is derived as shown in (9). This equation is transformed as the equation (11). By using F. Schultz-Grunow's experimental results, I calculated the constants as shown in (14). The mean velocity is calculated from (8), which is expressed in (12). The velocity distribution is shown in Fig.2. The other particular case is expressed by the equation (15), from which (17) is derived. This equation is the same as that derived by von Karman if α=1. From F. Schultz-Grunow's experimental results, I calculated the constants as follows: α=0.25. A=51.1, B=64.8.
- 宇宙航空研究開発機構の論文
- 1941-08-00
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