Geometry And Numerical Grids

A schematic diagram of the geometry is shown in Figure 2.1. It has a rectangular cross section with channel aspect ratio AR = 4:1. 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 (Lj/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 V-shaped 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.

Figure 2.1. Geometry of AR = 4:1 rectangular duct with V-shaped ribs.

Figure 2.2 shows the computational grid for the 4:1 rectangular duct around the V-shaped ribs. The grid was generated using an interactive grid generation code GRIDGEN. It was then divided into five overlapped chimera grid blocks to facilitate the implementation of the near-wall turbulence model and the specification of the boundary conditions. To provide adequate resolutions of the viscous sublayer and buffer layer adjacent to a solid surface, the minimum grid spacing in the near-wall region is maintained at 10-3 of the hydraulic diameter which corresponds to a wall coordinate y+ of the order of 0.5. The number of grid points in the streamwise direction from inlet to outlet is 394, while 33 x 75 grid points were used in the cross-stream plane. In all calculations, the root-mean-square (rms) and maximum absolute errors for both the mean flow and turbulence quantities were monitored for each computational block to ensure complete convergence of the numerical solutions and a convergence criterion of 10-5 was used for the maximum rms error.

Figure 2.2 Computational grid of AR = 4:1 rectangular duct with V-shaped ribs.
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