DNS 1-2 Quantification of Resolution

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Quantification of Resolution

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Quantification of resolution

Mesh resolution

The grid resolution corresponds to uniform $\Delta x^{+}=12.2,\ \Delta z^{+}=6.3$ and ranges from $\Delta y^{+}=0.16$ near the wall (first solution point) to $\Delta y^{+}=4.6$ at the centre of the channel. The near-wall Kolmogorov length scale, $\eta =\left({\bar {\rho }}\nu ^{3}/\epsilon \right)^{1/4}$, in wall units is $\eta ^{+}=1.54$.

Solution verification

The solution accurately captures the near wall and log-law behaviour of averaged streamwise velocity profile as shown in Fig. 2.

Figure 3: Average streamwise velocity, $Re_{\tau }=180$, vs data from Moser et al. (1999)

The turbulent stress profiles, shown by the solid lines, and the turbulent kinetic energy profile, represented by the dashed line, in figure 4 agree well with the data from Moser et al., which is indicated by the markers.

Figure 4: Turbulent stress profiles

The expected near wall behaviour of turbulent stresses are ${\widetilde {u^{\prime \prime 2}}},{\widetilde {w^{\prime \prime 2}}}\sim y^{2},\ {\widetilde {v^{\prime \prime 2}}}\sim y^{4}$ and ${\widetilde {u^{\prime }v^{\prime }}}\sim y^{3}$. These stresses near the wall from the current set of simulations are shown below.

• Figure 4: Near wall turbulent stress
• 

  ${\widetilde {u^{\prime \prime }u^{\prime \prime }}}$

• 

  ${\widetilde {v^{\prime \prime }v^{\prime \prime }}}$

• 

  ${\widetilde {w^{\prime \prime }w^{\prime \prime }}}$

• 

  ${\widetilde {u^{\prime \prime }v^{\prime \prime }}}$

The turbulent kinetic energy budget across the channel is also compared with data from Moser et al. (Fig. 5). The dashed black line denotes the residual of the budget.

Figure 6: Turbulent kinetic energy budget.

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Contributed by: Arun Soman Pillai — Imperial College London

Front Page

Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format

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