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Figure 1.4 Conceptual view of the secondary flow vortices induced by rotation, ribs, and channel orientation (dash line: rotation-induced vortices, solid line: rib-induced vortices).

Figure 1.4 shows conceptual views for the secondary flow patterns of a smooth and ribbed rotating two-pass rectangular channel. Fig. 1.4-a shows the smooth channel that rotates at b =90°

with respect to the direction of rotation. Two symmetric cells of counter rotating secondary flow (dotted line) appear due to Coriolis force. In the first pass of the channel, the fluid moves in a radially outward direction and the effect of Coriolis force directs the coolant from the core toward the trailing surface. This causes an increase of the heat transfer from the trailing surface and a decrease in the heat transfer from leading surface. However, in the second pass, the opposite situation can be seen that the fluid moves in a radially inward direction and the Coriolis force directs the coolant toward the leading surface, and causes an increase of heat transfer from the leading surface and a decrease in the heat transfer from trailing surface. When the channel is twisted to b=135° orientation, the secondary flow vortices are asymmetric and migrate diagonally away from the corner region of the inner-leading surface toward the center in the first passage, and from the corner region of the inner-trailing surface toward the center in the second passage. Figure 1.4-b shows the parallel arrangement is attached to the leading and trailing surfaces in a parallel fashion so that they are directly opposite to each other. The inverted 45° V-shaped ribs are attached to the leading and trailing surfaces in the first pass and 45° V-shaped ribs in the second pass. Also, it shows the secondary flow (dotted line) that induced by rotational forces and the secondary flow (solid line) induced by the inverted 45° V-shaped ribs in first pass and 45° V-shaped ribs in the second pass. As the channel angle changed to b=135°, the ribs secondary flow is not change, but the rotational secondary flows are shared between the principle surfaces (trailing, and leading) and side surfaces. Fig. 1.4-c shows the crossed rib case (the ribs on two opposite surfaces of the cooling channels are in crossed orientation). The cross orientation of the 45° V-shaped ribs coalesces the two pairs of the counter rotating secondary flow vortices to one pair of counter rotating secondary flow vortices. This reduction in number of secondary flow vortices limits the mixing between the near wall flow (hot fluid) and core flow

(cold fluid), which causes less heat transfer rate. In case of rotation, a pair of counter rotating secondary flow vortices appears and moves opposite to the counter rotating secondary flow vortices generated by cross ribs. This negative interaction minimizes the rotation effect by suppressing flow impingement on the first pass trailing and second pass leading surfaces and restrict mixing with the core for both leading and trailing surfaces in both passes, which causes low heat transfer performance.

Figures 1.5-7 show the regionally average Nusselt number ratios (Nu/Nuo) from leading and trailing surfaces for four Reynolds number (5000, 10000, 25000, 40000), rotating and non-rotating, and two channel orientations (b =90°, 135°).

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