Flatness factor

Fig. 6 Distribution of skewness and flatness factors for the streamwise vorticity fluctuations. A Kreplin and Eckelmann (21). From (22)...

It is desirable to obtain the result of statistical analysis of the digitized data for more detailed understanding of turbulence mechanism in a drag reducing pipe flow. Thus, in this work, we attempted to give a more quantitative analysis including the skewness factor and the flatness factor. 

Compared with the bubble characteristics, the information on the liquid flow characteristics specified by the axial and radial mean velocities, u and v, the root-mean-square values of the axial and radial turbulence components, m and the Reynolds shear stress u V, and higher correlations of turbulence components, such as the skewness and flatness factors, are limited except for a water-air system [8-12]. 

The magnet probe is applicable to molten metal flows at a temperature lower than the Curie point of the permanent magnet. Previous magnet probe measurements for a Wood metal bath were carried out by Xie et al. [23] at bath temperatures lower than 150°C. The magnet probe used by Xie et al. cannot detect the axial and radial velocity components simultaneously. Accordingly, data on the Reynolds shear stress and higher order turbulence correlations, such as the skewness and flatness factors, have not been published. 

The bubble characteristics, represented by the bubble frequency /b, gas holdup a, mean bubble rising velocity b, and mean bubble chord length Lb, were measured mainly on the y—z plane with a two-needle electroresistivity probe. Water velocity was measured with a two-channel laser Doppler velocimeter [25], The locations at which measurements were made were chosen by reference to the results for the bubble characteristics. The characteristics of water flow were represented by the vertical mean velocity u, the root-mean-square value of the vertical turbulence component w rms, and the skewness and flatness factors of the vertical turbulence component, and F . Data aquisition time was 600 s for each position. 

High-order turbulence correlations such as skewness and flatness factors are commonly introduced to understand the detailed structure of turbulence. The skewness factor Su and the flatness factor for the vertical turbulence component, are... 

The flatness factor F is nearly independent of the wettability of the plate. These measurements for and F differ from their respective values for a Gaussian distribution (5 = 0 and F = 3). Such discrepancy is associated with the turbulence production in the wake of bubbles. 

It is especially useflil for liquid samples in flat cells, which may extend through tlie entire height of the cavity. In the cylindrical cavity a TEq mode is frequently used because of its fairly high g-factor and the very strong along the sample axis. 

For a two-factor system, such as the quantitative analysis for vanadium described earlier, the response surface is a flat or curved plane plotted in three dimensions. For example. Figure 14.2a shows the response surface for a system obeying the equation... 

Although the Rockwell test is intended to be used on flat parallel-sided specimens, its use can be extended to rounded surfaces by using a curvature correction factor. Compound surfaces such as gear teeth can be tested but the results must be corrected for curvature. 

The cost of a PV device is determined by several factors. These include the kind of materials used and the amount of materials requited, choice of substrates, device design, and fabrication processes. Crystalline devices ate generally mote efficient, but thin-film devices ate anticipated to cost less in flat-plate configurations. The use of concentrated light permits retention of efficiency with simultaneous reduction in cost. 

Similarity Variables The physical meaning of the term similarity relates to internal similitude, or self-similitude. Thus, similar solutions in boundaiy-layer flow over a horizontal flat plate are those for which the horizontal component of velocity u has the property that two velocity profiles located at different coordinates x differ only by a scale factor. The mathematical interpretation of the term similarity is a transformation of variables carried out so that a reduction in the number of independent variables is achieved. There are essentially two methods for finding similarity variables, separation of variables (not the classical concept) and the use of continuous transformation groups. The basic theoiy is available in Ames (see the references). 

Indusirial Power Engineering and Applications Handbook Table 8.5 Service Factors for flat and V-belts... 

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