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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 timeaveraged ﬂow quality, x.
2. Compute the timeaverage superﬁcial velocities, {jf } and {jg }.
3. Compute the volumeaveraged void fraction, < α >, over the entire length of the tube. Is
this the same as {α} = {α}?
4. Compute the timeaveraged volumetric fraction, {β }.
5. Compute the timeaveraged static quality xst .
6. Compute the timeaverage phase velocities: {vf }f and {vg }g .
7. Compute the slip ratio, S .
8. Plot the instantaneous areaaveraged void fraction {α} at some arbitrary axial location as a
function of time. ...
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This note was uploaded on 10/22/2011 for the course ENU 4134 taught by Professor Schubring during the Fall '11 term at University of Florida.
 Fall '11
 Schubring

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