2 Description Of Problem

A schematic diagram of the geometry is shown in Figure 3.1. It has a rectangular cross section with channel aspect ratio, AR, of 4:1. Two geometries are investigated, one with smooth walls (Figure 3.1a) and the other one with ribs (Figure 3.1b). Two of the four side walls, in the rotational direction, are denoted as the leading and trailing surfaces, respectively, while the other two side walls are denoted as the top and bottom surfaces. The channel hydraulic diameter, Dh, is 0.8 in (2.03 cm). The distance from the inlet of the channel to the axis of rotation (Y-axis) is given by Rr/Dh = 20.0 and the length of the channel is given as L/Dh = 22.5. The channel consists of unheated starting smooth length (L1/Dh= 9.92), heated smooth or ribbed section (L2/Dh= 7.58) and unheated exit smooth section (L3/Dh=5.00). The arc length S is measured from the beginning of the heated section to the end of it. In the ribbed section, the leading and trailing surfaces are roughened with nine equally spaced ribs of square cross section. The rib height-to-hydraulic diameter ratio (e/Dh) is 0.078 and the rib-pitch-to-height ratio (P/e) is 10. All ribs are inclined at an angle a = 45° with respect to the flow. Two channel orientations are studied: (5 = 90° corresponding to the mid-portion of a turbine blade and (5 = 135° corresponding to the serpentine passages in the trailing edge region of a blade. A summary of the cases studied is given in Table 3.1.

Table 3.1: Summary of cases studied, Re = 10,000.





Ap p


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