Numerical simulation of turbulent drag reduction using micro-bubbles

By Jin Xu, Martin R. Maxey, G. Em Karniadakis. Journal of Fluid Mechanics, 2002

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Direct numerical simulations of gas/liquid multiphase flows (2011, background): “Recently, however, Pan and Banerjee (1997) and Xu et al. (2000) have introduced methods where the particle is spread over a few grid points and the effect of the particle on the fluid and the interactions between particles are partially accounted for.”
Friction Drag Reduction of External Flows with Bubble and Gas Injection (2010, background): “Advances in high-fidelity computation of multiphase flows now permit the detailed investigation of bubble-flow interactions in the context of BDR. Recent work includes that of Xu et al. (2002) and Ferrante & Elghobashi (2004, 2005), who employ Eulerian-Lagrangian models with point-force coupling.”
Bubbly and Buoyant Particle–Laden Turbulent Flows (2020, methodology): “Recent numerical works include those due to Xu et al. (2002) and Ferrante and Elghobashi (2004) employing Eulerian-Lagrangian models, and those due to Lu et al. (2005) using DNS to reveal how bubbles can modify the near-wall vortical structures causing friction drag reduction even with relatively…”
Frictional drag reduction by bubble injection (2014, unknown): “Xu et al. (2002) simulated the drag reduction performance provided by spherical bubbles in a DNS for a turbulent channel flow.”