*5.1. Flow Structures*

Figure 11 shows the turbulent structures in the cooling channel studied by using iso-surfaces of the velocity gradient tensor based on the λ2-criterion [33] colored by the magnitude of the mean velocity. The turbulent structures shown in this figure are dominated by three flow mechanisms and their interactions, and they are as follows: (1) horseshoe vortices about each pin fin; (2) jet impingement on the leading edge of each pin fin; and (3) the recirculating flows in the wake of each pin fin due to flow separation. Of these, the recirculating flows in the wake were found to be the most affected by heat load. At all heat loads, recirculating flows about pin fins in the first row did not shed. At low heat loads, those recirculating flows shed for pin fins in the second and higher rows. However, at high heat loads, those recirculating flows did not shed until the third row of pin fins. This is because when the heat load was high, the temperature of the air in the recirculating flows about second-row pin fins was significantly higher than the temperature of the air that flowed around them. With higher temperature, density is lower. As a result, even though the magnitudes of the velocity of the recirculating flows and the flow around them were similar where they interacted, the momentum of the recirculating flows was significantly less and so could not shed. When recirculating flows did shed, the vortical structures created were large. At low heat loads, the large vortical structures broke up into clusters of smaller-scale structures by the third and fourth pin fins. However, at high heat loads, this breakup did not occur until the fifth-row pin fins. High heat loads delayed breakup because they reduced density, which increased velocity magnitude and acceleration, and acceleration reduced turbulence. Thus, high heat loads reduced mixing and heat transfer by delaying the shedding and breakup of the large-scale vortical structures. Additional details of the flow field can be found in Lee & Shih [23].

Figure 12 shows the mean streamwise velocity contours and profiles (*u*∗) as a function of heat load. From this figure, it can be seen that the magnitude of the streamwise velocity increased as the heat load increased. This is because increasing the heat load increased the cooling flow's bulk temperature, which reduced its density and hence increased its velocity. Though the velocity magnitude of the flow increased with heat load, the velocity gradient next to the wall decreased as heat load increases. This is because heating causes expansion. This expansion also created jet-like flows about each pin fin, and the strength of the jet increased with heat load.

Figure 13 shows the mean temperature distributions (*T*∗) along the cooling channel as a function of heat load. From this figure, higher heating loads can be seen to lead to not just higher temperature in the flow but also higher temperature gradients in the thermal boundary layers. In addition, because of the expansion of the cooling air next to the walls, the thicknesses of the thermal boundary layer increased with increases in heat load.

Figure 14 shows the velocity fluctuations—streamwise, wall normal, and spanwise—at three heat loads. From Figure 14a, it can be seen that the streamwise fluctuating velocity (*u*∗ *rms*) about the pin fin decreased as the heat load increased for the first two rows of pin fins. This is because the flow there was highly accelerated by the expansion of the cooling air created by heating, and acceleration dampens turbulence. However, once shedding started about the pin fins in the third row, streamwise fluctuating velocity about the pin fin increased as the heat load increased. In the region midway between pin fins, the effect of heat loads was less because most of the acceleration created by the heating occurred near the pin fins. Figure 14b shows that heating of the endwall increased velocity fluctuation normal (*v*∗ *rms*) to the wall as the heat load increased. This was caused by the expansion of the air and jet-like flow created by the heating. However, like streamwise velocity fluctuation, normal velocity fluctuation about pin fins in the second row decreased as the heat load increased, but increased with the heat load once shedding started. Figure 14c shows that the spanwise velocity fluctuations (*w*∗ *rms*) had the same trend as the normal velocity fluctuations (*v*∗ *rms*).

**Figure 11.** *λ*2-criterion colored by magnitude of mean velocity.

**Figure 12.** Mean streamwise velocity contours and profiles for Tw/Tc = 1.01 (NH), 2.0 (MH), and 4.0 (SH).

**Figure 13.** Mean temperature contours and profiles for Tw/Tc = 1.01 (NH), 2.0 (MH), and 4.0 (SH).

**Figure 14.** Root-mean square (rms) of the (**a**) streamwise, (**b**) wall normal, and (**c**) spanwise fluctuating velocities as a function of heating load.

Figure 15 shows the variance of the temperature fluctuation (*T* ∗). With Tw/Tc = 1.01 (NH), there was no temperature variance as expected. As Tw/Tc increased, the fluctuating temperature got higher, particularly in the near-wall region, where the mean temperature gradient was also large. For the moderate and strong heating cases, the peak temperature fluctuations next to the endwall increased steadily along the channel. After pin fins in the fourth row, the mean temperature and the normalized temperature fluctuation became periodic from row to row.

**Figure 15.** Temperature variance profiles for NH, MH, and SH wall heating.
