A resistor-network-inspired eddy viscosity model for non-linear turbulence modulation in bubbly flows

The shed turbulent eddies from the wake of bubbles lead to the presence of bubble-induced turbulence (BIT) in gas-liquid two-phase flow. BIT not only competes intensively with shear turbulence (ST) for local dominance in time and space, but more importantly, BIT and ST together contribute to the entire liquid phase turbulence. It is known that their individual contributions and interactions can be reflected in the kinetic energy spectrum of turbulence, with a slope of −5/3 when ST dominates, while the slope becomes −3 when BIT takes control. However, questions still remain about how mesoscale structures, such as eddies due to BIT, interact with shear turbulence to modulate the liquid phase turbulence. For turbulence modeling, the effects of BIT are usually expressed by the linear superposition of a turbulent viscosity term or source terms on the basis of the single-phase Reynolds-Averaged Navier–Stokes (RANS) equations. Inspired by a resistor-network analogy, the present work draws an analogy between turbulent eddy viscosity and the series & parallel resistors, which leads to a non-linear superposition model of the turbulent eddy viscosity closure for turbulent bubbly flows. Due to the intermittency of BIT, the proposed non-linear turbulent viscosity closure model can account for the cumulative effect of wake attenuation. Comparative examination of simulation results among different BIT models reveals that an appropriate mathematical depiction of the non-linear superposition of turbulent viscosity components is essential for accurately reflecting the turbulence modulations induced by the interplay of BIT and ST.