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Complementary Solution to Analysis of Energy Dissipation
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Distribution
From previous section, we concluded the uniformity of energy dissipation rate using visual investigation. This section presents the results using a statistical method to complement the result from previous section.
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Figure 1. Contour of Energy Dissipation Rate (h/b=3)
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Figure 1 shows the visually the distribution the contour of the energy dissipation rate. Visually, we can judge the uniformity of the energy dissipation rate for the given geometry. A less subtle subjective way of characterize characterizing the uniformity of the energy dissipation rate is to use UDF to analyze and plot out the distribution of the energy dissipation rate. The UDF script can he access here.
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Figure 2. Distribution of Energy Dissipation Rate (h/b=3) with "hump"
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By plotting Figure 2 shows the distribution according to the range of energy dissipation rate shown in figure 1, we are able to better characterize the distribution of the energy dissipation rate in figure 2. It is interesting to see . Note that there is a hump in the distribution. The peak of the hump is around energy dissipation rate of 0.006 m2/s3. There might be relationship between the hump and the uniformity of the energy dissipation rate.
Smaller range of energy dissipation rate was set to investigate this regionrelationship.
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Figure 3. Contour of Energy Dissipation Rate (h/b=3) with Tighter Range
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From figure 3, setting a tighter range of energy dissipation rate, we see that the contour is dominated by the blue and green region which is from the range of 0.005 to 0.01 m2/s3. This explains the hump in the appearance of hump in figure 2.
To further investigate this phenomena, another flocculation geometry with flocculation tank height of 4b is plotted.
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Figure 4. Distribution of Energy Dissipation Rate (h/b=4) with "hump"
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Figure 5. Contour of Energy Dissipation Rate (h/b=4)
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Figure 4 shows the distribution of energy dissipation rate for flocculation tank height of 4b. We also see a visible hump.
Figure 5 shows the uniformity of energy dissipation rate with flocculation tank height of 4b.
Since hump appears both in the geometry of uniform energy dissipation rate, we concluded that hump in the distribution of energy dissipation rate provided by UDF will be a good indication of uniformity of energy dissipation rate.
Figure 6.Distribution
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of Energy Dissipation Rate (h/b=
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10)
From figure 5For flocculation tank height of 10b, we see that the contour is dominated by blue and green region ranges from 0.002 to 0.006 which further explain the visibility of hump. With two example, we have verifed that the hump is a good parameter is analyzing uniformity of the energy dissipation rate, we can use this characteristic in determining energy dissipation rate for different geometry.
there is no visible hump. From previous analysis, this tell us that the energy dissipation rate in the flocculation tank is not uniform.
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Figure 7. Contour of Energy Dissipation Rate (h/b=10)
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Figure 7 clearly shows the non-uniformity in energy dissipation rate for such geometry.