**2.6.3 Single-phase flow**

For comparison, a long simulation without bubbles was also conducted at the same channel Reynolds number of 3786 and Prandtl numbers of 2,1Pr*<sup>c</sup>* . The computational conditions are summarized in Table 6. Statistical quantities were obtained by taking averages over the period of about 30,000 in wall units. The time-averaged friction Reynolds number was 127.2 as in Lu and Tryggvason (2008).


Table 6. Computational conditions for the single-phase flow


Table 7. Computational conditions for the centered 2nd-order scheme.

In order to estimate the effects of the numerical diffusion caused by the QUICK scheme, a simulation was conducted by using the centered 2nd-order scheme (consistent scheme) for the convection terms in a staggered grid system (Kawamura et al., 1998). It is found that the amplitude of the streamwise component of vorticity is slightly (about 1.5%) lower in the
