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Averaging_Example_StudentWork

# Averaging_Example_StudentWork - An Example of Averaging...

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Unformatted text preview: An Example of Averaging Parameters 1 Air and water ﬂow at high pressure (about 80 atmospheres) in a round tube. A slug ﬂow forms. The geometry – cylindrical slugs of gas along the centerline, liquid everywhere else – is shown below. Assume upﬂow as shown. Assume a single gas velocity and a single liquid velocity applies everywhere. Diameter: 0.0071 m Diameter: 0.01 m 0.02 m 0.08 m Given the following (take phase densities as constants and mass ﬂow rates as time averages). ρg = 100 kg m−3 (1) (2) −1 ρf −3 (3) = 1000 kg m mg = 0.005 kg s ˙ mf ˙ −1 = 0.05 kg s (4) Assume the gas slugs are coherent, periodic structures – they all travel at the same speed and keep constant distance between one another. Compute the following: 1. Compute the time-averaged ﬂow quality, x. 2. Compute the time-average superﬁcial velocities, {jf } and {jg }. 3. Compute the volume-averaged void fraction, < α >, over the entire length of the tube. Is this the same as {α} = {α}? 4. Compute the time-averaged volumetric fraction, {β }. 5. Compute the time-averaged static quality xst . 6. Compute the time-average phase velocities: {vf }f and {vg }g . 7. Compute the slip ratio, S . 8. Plot the instantaneous area-averaged void fraction {α} at some arbitrary axial location as a function of time. ...
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