Fluid mixing in a T-shaped micro-mixer

Investigation of the steady engulfment regime in a three-dimensional T-mixer

“…This is in agreement with the numerical results in Galletti et al, 6 which localize the onset of engulfment in the interval 140 < Re < 192 and is exactly the same result as that indicated in Orsi et al 10 for the same case. This is also in excellent agreement with Engler et al 2 (Re = 147), Bothe et al 3 (Re = 146), and Hoffmann et al 4 (Re = 135-150), who used slightly different geometries.…”

“…In the present simulations, the lengths of the inflow and outflow pipes are L i = 6.875 and L o = 12.5, and the incoming flow is assumed to have a fully developed (unidirectional) laminar profile for the considered rectangular cross-section. 3 The same flow studied here has been investigated in Galletti et al,6 where it is shown that the considered lengths of the pipes are sufficient for a proper prediction of the steady engulfment instability.…”

“…This clearly leads to a significantly larger mixing than in the previous regimes. If the Reynolds number is further increased, the flow may become unsteady (see, e.g., Bothe et al, 3 Dreher et al, 5 and Galletti et al 6 ). For instance, for square inlet pipes and an outflow pipe width (W o ) to height (H) ratio W o /H = 2 and for fully developed inlet velocity conditions, Engler et al 2 show that the flow is in stratified regime approximately for Re < 50 (based on the outflow hydraulic diameter and mean velocity), in vortex regime for 50 < Re < 150, engulfment starts at Re 150 and the flow is periodic for 240 < Re < 400.…”

“…Although a plane mixer may be an interesting configuration for detailed theoretical analysis, the attention in the literature is mainly focused on 3D configurations with rectangular sections of the pipes for their practical interest. For this kind of mixers, three different working regimes have been identified in experiments and simulations available in the literature, depending on the flow Reynolds number (see, e.g., Engler et al, 2 Bothe et al, 3 and Hoffmann et al 4 ). At very low Reynolds numbers, the two streams coming from the inlet pipes remain completely segregated even in the outflow pipe (stratified flow) and mixing is only due to diffusion.…”

“…Many works in the literature are dedicated to characterize, in particular, the steady engulfment regime and to investigate the flow conditions for its onset. Bothe et al 3 investigate mixing properties in the engulfment regime through numerical simulations and provide validation against experimental data. An experimental investigation is documented in Hoffmann et al 4 In Soleymani et al 7 an empirical equation is proposed to determine the critical Reynolds number for the engulfment as a function of the channel geometry, by extrapolating a set of numerical simulations.…”