DNS 1-3 Quantification of Resolution

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Quantification of Resolution

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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. 16 and 17 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.

Reynolds stress equations budgets

The Reynolds stress equations and the turbulent kinetic energy equation budget terms are discussed in this section. The first step is to show that Alya can close the budgets. To this aim, the figures below show the turbulent kinetic energy equation budgets and the Reynolds stress streamwise direction budget in a channel flow at ${Re_{\tau }=180}$. The results are compared with the DNS data of Hoyas and Jimenez (2008) (in circles) and Moser et al. (1999) (in triangles) that can be found freely available online. As it can be seen, the residuals close well within an order of magnitude with respect to the production. This proves that the methodology used in this entry is sound and that Alya can close the budgets if given the necessary grid resolution and integration time.

Figure 11: Channel flow ${Re_{\tau }=180}$, Alya DNS-8M DoF, TKE and stream-wise Reynolds stress budget terms comparing with Hoyas and Jimenez (circles) and Moser, Kim and Mansour (triangles).

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.

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

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Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

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