Abstract-
For moderate Reynolds numbers, the isotropic relation
between second-order and third-order moments for velocity increments
(Kolmogorov's equation) is not respected, reflecting a non-negligible
correlation between the scales responsible for the injection, transfer and
dissipation of the turbulent energy.
For (shearless) grid turbulence, there is only one dominant large-scale phenomenon, which is the non-stationarity of statistical moments resulting from the decay of energy downstream of the grid. In this case, the extension of Kolmogorov's analysis, as carried out by Danaila et al. (1999) is quite straightforward. For shear flows, several large-scale phenomena generally coexist with similar amplitudes. This is particularly the case for wall-bounded flows where, except on the axis of a channel flow, turbulent diffusion and shear effects are of comparable amplitude. These large-scale effects are taken into account in a quasi-homogeneous context. The objective of our work is to quantify, for a fully developed turbulent channel flow, the influence of these two effects on the scale-by-scale energy budget in order to derive a generalized Kolmogorov equation. Relatively good agreement between the new equation and hot-wire measurements is obtained in the outer region (40 < y+ <150) of the channel flow.
Also investigated is the near-wall region of a plane channel liquid flow, for variable Reynolds numbers. Using the electrochemical method, we study experimentally a high Schmidt passive scalar mixing (Sc ≈ 1000), for which the diffusion layer is situated in the viscous sublayer. The scalar field is maintained by a mean gradient, imbedded in a strongly sheared velocity field. For moderate Reynolds numbers, the passive scalar derivative (along, and perpendicular to the mean scalar gradient) skewness is around 1. For higher Reynolds numbers, the scalar gradient skewness approaches zero, consistent with the reduction of small-scale anisotropy of the small-scale scalar. In conclusion, for a fixed Sc number, the mixing becomes more isotropic for increasing Reynolds number.
Our results are critically compared with those published in the literature and with those obtained for a mixing characterized by a Sc∼1 (see figure).
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| Velocity field (measured by PIV, two components) and air/fuel mixing (PLIF) in a "model experience" of a HCCI (Homogeneous Charge Compression Ignition) engine. The Schmidt number of the mixing air/(vaporized) fuel is Sc∼1.3. |
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