NUCE502 Homework 4 Name: Score : of 100 1. (60 pts) Consider a vertical-upward air-water two-phase flow in a round pipe with 2.54 cm inner diameter. Assume that the flow is operating at 25 °C under atmospheric pressure condition. Use any graphing software and generate the two-phase flow regime map proposed by Mishima and Ishii (1984). Submit both the flow regime map showing four regime transition boundaries and a screen shot of the spreadsheet as part of the solution. Hint: In plotting the map, use logarithmic scale for both jg and jf (x and y axes, respectively) ranging from 0.01 m/s to 100 m/s. In estimating the distribution parameter for the drift-flux model, use C0 =1.2 0.2 - r r g f . 2. (40 pts) Prediction for flooding phenomenon can be made for various combinations of liquid and gas flow rates by identifying tangential lines at the flooding points in the graph of jgf vs. α . Given that jgf is correlated with α by: jgf = α (1−α)n vr∞ , the "flooding line" can be generated when one plots flooding solutions in jg vs. jf graph for varying void fractions by employing the following relations: jg = α 2vr∞n(1−α)n−1 and j f = −(1−αn)vr∞ (1−α)n (1) (a) (20 pts) Derive Eq. (1) by using the analogy of identifying tangential lines at the flooding points in the graph of jgf vs. α . (b) (20 pts) For a bubbly flow of a certain mixture, it is given, that n=1.1 and the terminal velocity vr ∞ is 30.0 cm/s. Using any graphing software, plot jg vs. jf (in y and x axes, respectively) for varying void fractions to obtain flooding lines.