Abstract
Data from direct numerical simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. We developed a new method, based on an extension of the barycentric map approach, that allows us to quantify and visualize the anisotropy and componentiality of the flow at any scale. Using this we found that the bubbles significantly enhance anisotropy in the flow at all scales compared with the unladen case, and that for some bubble cases, very strong anisotropy persists down to the smallest scales of the flow. The strongest anisotropy observed was for the cases involving small bubbles. Concerning the energy transfer among the scales of the flow, our results indicate that for the bubble-laden cases, the energy transfer is from large to small scales, just as for the unladen case. However, there is evidence of an upscale transfer when considering the transfer of energy associated with particular components of the velocity field. Although the direction of the energy transfer is the same with and without the bubbles, the behaviour of the energy transfer is significantly modified by the bubbles, suggesting that the bubbles play a strong role in altering the activity of the nonlinear term in the flow. The skewness of the velocity increments also reveals a strong effect of the bubbles on the flow, changing both its sign and magnitude compared with the single-phase case. We also consider the normalized forms of the fourth-order structure functions, and the results reveal that the introduction of bubbles into the flow strongly enhances intermittency in the dissipation range, but suppresses it at larger scales. This strong enhancement of the dissipation-scale intermittency has significant implications for understanding how the bubbles might modify the mixing properties of turbulent flows.
Highlights
Turbulence and multiphase flows are two of the most challenging topics in fluid mechanics and when combined they pose a formidable challenge, even in the dilute dispersed regime (Balachandar & Eaton 2010)
Turbulence arising from this relative motion is often referred to as bubble-induced turbulence (BIT) and its effects can be captured in the Reynolds-averaged Navier–Stokes modelling framework through the inclusion of additional source terms in the relevant transport equations (Fox 2014; Joshi & Nandakumar 2015; Ma 2017; Liao et al 2019; Ma, Lucas & Bragg 2020a)
A similar finding concerning an average forward energy cascade was reported by Lai et al (2018), who performed direct numerical simulation (DNS) of bubbles rising vertically in a channel flow filled with initially quiescent water
Summary
Turbulence and multiphase flows are two of the most challenging topics in fluid mechanics and when combined they pose a formidable challenge, even in the dilute dispersed regime (Balachandar & Eaton 2010). The study of Pandey et al (2020) was based on Fourier space analysis with averaging over spherical shells in wavevector space, and so did not permit them to explore the anisotropy of the flow at different scales Another important point is that, in Pandey et al (2020), the flow had no background turbulence (i.e. all the turbulence was generated by the bubbles), and it was not possible to consider how the bubbles modify the turbulence compared with the single-phase case. These results provide new insights into the properties of bubble-laden turbulent flows, and how they differ from the single-phase counterpart at different scales in the flow
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