*4.1. LES of Flow in Channel without Pin Fins*

To ensure that the synthetic turbulence inflow BC imposed at x = −15D could provide the correct turbulent flow to enter into the test section with pin fins at x = 0, three grids were examined along with time-step sizes that would yield stable and accurate solutions. The three grids used, denoted as coarse, baseline, and fine, are shown in Figure 2 and summarized in Table 2. Note that h-refinement was used when finer resolution was needed next to the wall to maintain a consistent aspect ratio as the grid is refined. The coarse grid in the LES region from x = −100D to x = 0 consisted of 1.64 million cells with maximum/minimum non-dimensional cell spacings of 16/16 in the streamwise direction, 13.9/0.9 in the wall-normal direction, and 16/16 in the spanwise direction. The baseline grid consisted of 2.79 million cells with max./min. non-dimensional cell spacings of 16/8, 13.7/0.5, and 16/8 in the streamwise, wall-normal, and spanwise directions, respectively. The fine grid consists of 5.08 million cells with max./min. cell spacings of 16/4, 13.5/0.3, and 16.4/0.3 in the streamwise, wall-normal direction, and spanwise directions, respectively. Here, it is noted that the region upstream of the LES region (x = −115D to −15D), where RANS with the SST model was used to provide the "fullydeveloped" mean flow at x = −15D for the LES region, had a grid with 2.5 M cells. This

grid provided grid-independent solutions for the RANS region, where the first cell next to the channel walls had y+ less than unity, and there were five cells within y+ of five.

**Figure 2.** Grids used for LES of flow in the test section without pin fins.



Figure 3 shows the mean flow profiles normalized by the friction velocity at Reτ = 365 obtained by using the coarse, baseline, and fine grids along with results from DNS [30] and experimental measurements [31]. From this figure, the solution from the coarse grid can be seen to overpredict the DNS and experimental data in the log-law region with y+ between 10 and 100, indicating inadequate resolution in the near-wall region. Solutions from both the baseline and fine grids were in good agreement with the log-law equation and the DNS and experimental data.

**Figure 3.** Mean flow profiles normalized by friction velocity at Reτ = 365.

Figure 4 shows the Reynolds stress and the streamwise and spanwise velocity fluctuations normalized by the friction velocity. The solution from the coarse grid can be seen to overpredict the DNS data, whereas solutions from the baseline and fine grids match well.

**Figure 4.** Mean flow fluctuations normalized by friction velocity at Reτ = 365.

Figure 5 shows the power spectrum of turbulent kinetic energy at (x, y) = (56.25H, 0.5D) in the "fully-developed" region of the channel obtained by the baseline grid. The spectrum in the inertial subrange follows the Kolmogorov's −5/3 energy decay slope, indicating that most of the energetic large-scale eddies were resolved by the grid. According to these comparisons, the baseline grid had sufficient near-wall resolution to resolve the turbulent boundary layer and required less computation costs than the fine grid. Thus, the grid resolution based on the baseline grid was used for all LES simulations in the region between x = −15D and x = 0.

**Figure 5.** Energy spectrum at (x, y) = (56.25H, 0.5D) obtained by the baseline grid.

#### *4.2. LES of Flow in Channel Flow with Pin Fins*

Figure 6 shows a close-up view of the grid used in the test section with pin fins. As shown in the figure, a wrap-around grid was used about each pin fin. Also, grid points were clustered to all solid surfaces. The grid spacings used were guided by the "baseline grid" described in the previous section to ensure that the turbulent structures about all solid surfaces were adequately resolved, including those about pin fins. Table 3 summarizes the grid spacings and time-step sizes used for all the LES cases performed. Note that the grid spacings and time-step sizes had to be reduced to get the required spatial and temporal accuracy when the heating load was increased.

**Figure 6.** Grid used in the test section with pin fins.



Figure 7 shows the power spectra of turbulent kinetic energy at (x/D, y/D, z/D) = (5, 1, 0) and (10, 1, 0) behind Pin 2 and Pin 4 at different heating loads. In the figure, the energy spectra can be seen to follow the Kolmogorov's -5/3 energy decay slope in the inertial subrange before their cut-off wave numbers.

**Figure 7.** Energy Spectra obtained with different heating loads at x/D = 5 and 10.

To further assess the grid resolutions, the index of resolution quality for LES, *LESIQν*, introduced by Celik et al. [32], given by the equation below was computed:

$$LESI\_{\nu} = \frac{1}{1 + 0.05 \left(\frac{(\mu + \mu\_{SCS})}{\mu}\right)^{0.53}} \tag{2}$$

Figure 8 shows the *LESIQ<sup>ν</sup>* distributions from the LES solutions obtained under three levels of heating. Since the minimum value of *LESIQν* is 0.94, which is higher than 0.8, it shows that the grids used were able to resolve a significant portion of turbulent kinetic energy.

**Figure 8.** Celik's index of resolution quality for the LES solutions generated.

To validate the LES solutions, the results generated were compared with the experimental data of Ames & Dvorak [9–11]. Figure 9 shows a comparison between computed and measured turbulent boundary layer profiles normal to the pin-fin wall and normal to the endwall. From that figure, LES can be seen to predict the mean flow velocity well with maximum relative difference less than 2%. Note that the profile normal to the pin-wall at Row#1 does show noticeable overprediction in the outer region with about 8% relative difference, but matches well to the near-wall region.

**Figure 9.** Measured and computed mean x-component velocity profiles with ReD = 10,000.
