Quantification of resolution

Mesh resolution

The mesh resolution is quantified by obtaining a relation between the mesh characteristic length ( ${\Delta }$ ) and the characteristics lengths, i.e., the Taylor microscale ( ${\eta _{T}}$ ) and Kolmogorov length scale ( ${\eta }$ ). The former relation is shown in Fig. 1 while the latter is reported in Fig. 2. As it can be seen, both relations indicate that the resolution achieved by the present grid is at DNS level. In particular, it is commonly accepted that DNS is achieved when ${\Delta /\eta _{T}\leq 5}$ , as shown in Fig. 2.

Figure 1: Stanford double diffuser, Alya DNS-250M DoF, relation between the mesh size and the Taylor microscale.

Figure 2: Stanford double diffuser, Alya DNS-250M DoF, relation between the mesh size and the Kolmogorov length scale.

Solution verification

This section aims to provide an insight on the dataset freely available in this wiki. Simulation results are compared with the DNS of Ohlsson et al. (2010) and the experimental data of Cherry et al. (2008). The grid resolution has been proven to be fine enough to be at DNS level. An animation of the fluctuations of this flow can be seen in this link.

Velocity profiles and RMS quantities

The 10000 Reynolds number diffuser has been simulated and compared with the results with previous DNS data from Ohlsson et al. (2010) and experimental data from Cherry et al. (2008). Fig. 3 and Fig. 4 show the averaged velocities and the RMS quantities along the characteristic lines of the diffuser for the experimental data and both DNS simulations. Finally, Fig. 5 and Fig. 6 show a comparison of the contours of the span-wise velocity and span-wise rms fluctuations respectively.

Figure 3: Stanford double diffuser, Re=10000, validation. Average velocities, Cherry et al. (2008) and Ohlsson et al. (2010) vs data obtained with Alya.

Figure 4: Stanford double diffuser, Re=10000, validation. Average streamwise velocity fluctuations, Cherry et al. (2008) and Ohlsson et al. (2010) vs data obtained with Alya.

Fig. 3 and Fig. 4 show a fair agreement between both numerical simulations, proving that the approach used is an optimal strategy. Moreover, the points where the DNS performed with Alya deviates from the results of Ohlsson et al. (2010), this is in favour to move closer to the experimental data of Cherry et al. (2008). Thus, a good agreement is also obtained with the experiment. The inclusion of a roughness element on the long inlet duct, to trigger the turbulence, is shown to have a negligible effect on the quality of the results.

Figure 5: Stanford double diffuser, Re=10000, validation. Average streamwise velocity contours, Cherry et al. (2008) and Ohlsson et al. (2010) vs data obtained with Alya. The positions of the contour slices are, from top to bottom, x/h=2, 5, 8 and 15.

Figure 6: Stanford double diffuser, Re=10000, validation. Average streamwise velocity fluctuation contours, Cherry et al. (2008) and Ohlsson et al. (2010) vs data obtained with Alya. The positions of the contour slices are, from top to bottom, x/h=2, 5, 8 and 15.

Other turbulent statistics

Other relevant statistics from the database are presented in this section. In particular, the turbulent kinetic energy (TKE) and the characteristic length scales (i.e., the Taylor micro-scale ${\eta _{T}}$ and the Kolmogorov length-scale ${\eta _{K}}$ ) are presented in Fig. 7 along some characteristic contours of the diffuser.

Figure 7: Stanford double diffuser, Re=10000. Turbulent kinetic energy (TKE), Taylor microscale and Kolmogorov lengthscale obtained with Alya on contour slices located, from top to bottom, at x/h=2, 5, 8 and 15.

Turbulent kinetic energy budget equation terms

The turbulent kinetic energy budget equation terms are presented in this section. As it can be seen in Fig. 9, the magnitudes of the residuals for the TKE budget equations is very small, of the order of ${10^{-2}}$ , which is deemed sufficient for the present case.

Figure 9: Stanford double diffuser, Re=10000. Turbulent kinetic energy (TKE) budget balance obtained with Alya on characteristic lines of the diffuser.

Contributed by: Oriol Lehmkuhl, Arnau Miro — Barcelona Supercomputing Center (BSC)

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