Quantification of resolution

Mesh resolution

The mesh resolution is quantified by obtaining a relation between the mesh characteristic length ( ${\Delta }$ ) and characteristic lengths of the turbulence, i.e., the Taylor microscale ( ${\eta _{T}}$ ) and Kolmogorov length scale ( ${\eta _{K}}$ ). The former relation is shown in Fig. 10 while the latter is reported in Fig. 11. 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 ${\Delta /\eta _{K}\leq 5}$ , as shown in Fig. 11.

Figure 10: Stanford double diffuser, Alya DNS-250M DoF, relation between the mesh size and the Taylor microscale.

Figure 11: Stanford double diffuser, Alya DNS-250M DoF, relation between the mesh size and the Kolmogorov length scale.

Solution verification

For verification of the quality of the results obtained in the present simulations, these are compared with those of the DNS of Ohlsson et al. (2010) and the experimental data of Cherry et al. (2008) (available in UFR 4-16 of the Wiki) and a check is made whether the residuals in the budget equations for the Reynolds stresses are sufficiently small.

===Velocity profiles and RMS quantities===

Figs. 12 and 13 presented in the next section (Statistical Data) show, respectively, the mean velocities and RMS values of the streamwise fluctuations along characteristic lines of the diffuser for the experimental data and both DNS simulations. Further, Figs. 15 and 16 show, respectively, a comparison of the contours of the streamwise mean velocity and its RMS fluctuations at selected cross sections of the diffuser. As can be seen, there is a fair agreement between the 2 numerical simulations providing confidence in the present simulations, and where these deviate locally from the results of Ohlsson et al (2010), the present results are closer to the experimental data of Cherry et al (2008) so that overall good agreement is obtained with these data. An impression of the fluctuations can be obtained from an animation that can be seen in this link. It should be noted that the inclusion of a roughness element in the long inlet duct in order to trigger turbulence has a negligible effect on the quality of the results.

Turbulent kinetic energy budget equation terms

The turbulent kinetic energy budget equation terms are presented in this section. Contour plots have been represented for each of the budget terms in Fig. 20 to Fig. 32. As it can be seen in Fig. 14 and the contour plots of the budget residuals in Fig. 33 and Fig. 34, 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.