Flow_Regime_Transition_and_K_H_Instability_Homework.pdf -...

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Josh Halsted NSE 667-Flow Regime Transition/K-H Instability HW June 8, 2020 Problem Statement For a rectangular channel ( H*W=1 m x 0.2 m ) flow with stratified water-air two-phase flow at atmospheric pressure and room temperature (1 bar and 20° C), the steady state solutions comes from Equations (1-59), (1-60), and (1-61) (in the notes). Assuming the functional form of 𝐹 is given by: 𝐹 (⟨𝛼 0 ⟩, ⟨⟨? ?0 ⟩⟩ , ⟨⟨? ?0 ⟩⟩) = 𝐹 ? + 𝐹 ? = 0 𝐹 ? = − 1 1 − ⟨𝛼 0 { 1 2 ? ?,? 𝜌 ? ⟨⟨? ?0 ⟩⟩ 2 [ 2(1 − ⟨𝛼 0 ⟩)𝐻 + 𝑊 (1 − ⟨𝛼 0 ⟩)𝐻𝑊 ] − 1 2𝐻 ? 𝑖 𝜌 ? (⟨⟨? ?0 ⟩⟩ − ⟨⟨? ?0 ⟩⟩) 2 } 𝐹 ? = 1 ⟨𝛼 0 { 1 2 ? ?,? 𝜌 ? ⟨⟨? ?0 ⟩⟩ 2 [ 2⟨𝛼 0 ⟩𝐻 + 𝑊 ⟨𝛼 0 ⟩𝐻𝑊 ] + 1 2𝐻 ? 𝑖 𝜌 ? (⟨⟨? ?0 ⟩⟩ − ⟨⟨? ?0 ⟩⟩) 2 } Where ? ?,? , ? ?,? and ? 𝑖 are water wall friction factor, gas wall friction factor, and interface friction factor, respectively. Assume that they are all equal ( ? ?,? , ? ?,? and ? 𝑖 = 0.002 ). Analyses (1) For a given void fraction ⟨𝛼 0 , find the liquid velocity slip ratio 𝑆 = ⟨⟨? ?0 ⟩⟩ / ⟨⟨? ?0 ⟩⟩ , and plot 𝑆 against ⟨𝛼 0 ⟩ ∈ (0,1) . ⟩⟩

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