Bubbly_Flow_Homework.pdf - Josh Halsted NSE 667-Bubbly Flow...

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Josh Halsted NSE 667-Bubbly Flow Homework May 5, 2020 1. In horizontal two-phase flows of air bubbles and water, which fluid moves faster, and why? For horizontal two-phase flow consisting of air bubbles and water with a pressure gradient along the pipe (similar to Hagen-Poiseuille flow), the bubble would potentially be born at the bottom of the pipe, then break off when it reached a sufficient size because the water “pulls off” the bubble from the pipe via viscous effects. The bubble would accelerate to the liquid velocity because of the drag force, which accelerates it in the flow direction. The bubble velocity would then surpass that of the mean liquid velocity because of the pressure force accelerating the bubble. To illustrate why, consider the Hagen-Poiseuille flow equation for a circular pipe: Δ𝑃 = 8𝜇𝐿𝑣 𝑅 2 For the liquid and air phase, the pressure change is equivalent across the length of the pipe: ( 8𝜇𝐿𝑣 𝑅 2 ) 𝑤𝑎𝑡𝑒𝑟 = ( 8𝜇𝐿𝑣 𝑅 2 ) 𝑎𝑖𝑟 𝑣 𝑎𝑖𝑟 𝑣 𝑤𝑎𝑡𝑒𝑟 = 𝜇 𝑤𝑎𝑡𝑒𝑟 𝜇 𝑎𝑖𝑟 = 8.9 ∗ 10 −4 1.81 ∗ 10 −5 = 49.17

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