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An analytical estimate of the energy dissipation rate in the dissipation cell can be obtained. Use the following equations: Include Page AGUACLARA:Gequalrootepsilonovernu AGUACLARA:Gequalrootepsilonovernu Include Page AGUACLARA:epsilonCpVsquaredover2theta AGUACLARA:epsilonCpVsquaredover2theta Include Page AGUACLARA:epsiloncell AGUACLARA:epsiloncell
Using the equation above to estimate the energy dissipation rate in the expansion zone we obtain an average value of ??. This is based on the assumption that the length of the dissipation region is approximately twice (Π cell = 2) the distance between the baffles.
Calculate the value of Gθ for each cell in the computational grid and sum this up over the domain containing the dissipation zone to get a more accurate measure of the actual Gθ for a 180 degree bend. Compare that with the estimate that the AguaClara team is currently using.Include Page AGUACLARA:Gthetacell AGUACLARA:Gthetacell
Figure 10. Wall Yplus
Figure 10 shows that the y+ values. According to FLUENT documentation "the mesh should be made either coarse or fine enough to prevent the wall-adjacent cells from being placed in the buffer layer (y+ = 5~30)". Since the y+ from the model was consistently less than five (in the viscous sublayer) the turbulence near the walls was resolved properly.
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The effect of the Reynolds number on the pressure coefficient drop was analyzed. This was done by changing the inlet velocity which initially produces a Reynolds number of 10,000. From figure 12, it can be seen that the value of the pressure coefficient drop has a small change when compared to big changes in Reynolds number. In other words, the pressure coefficient drop is not sensitive to the Reynolds number at the inlet. This implies that the design of the flocculator should not be altered by the inlet flow rate. This is to say that one flocculator design can be used for different flow ratesby the inlet flow rate. This is to say that one flocculator design can be used for different flow rates. You are right that the pressure coefficient is insensitive to Reynolds number. But that does not mean that a single flocculator can handle a wide range of flows. The energy dissipation rate is still proportional to the velocity cubed.
Figure 13. Clearance Height Effect on Pressure Coefficient Drop and Maximum Velocity
The effect of the clearance height on the pressure coefficient drop was also analyzed. It can be seen that the pressure coefficient drop is independent of the change in clearance height after the clearance height is greater than a critical value. Figure 13 shows that after a critical value of 1, the pressure coefficient drop is constant. This phenomena phenomenon can be explained by looking at figure 14 below. Figure 14 shows the turbulent dissipation rate for clearance heights of 0.1 m 1b and 1.5 m5b. It can be observed that the length of high maximum dissipation rate is equal for both reactors. This means that 0.1 m is the clearance height after which a stagnant fluid starts A recirculation zone begins to form at the bottom of the reactor when the clearance height is larger than 1b. A similar argument can be made for the values of maximum velocity. A clearance height less than 0.1 m 1b results in a higher pressure coefficient drop as it creates an 'unnatural' additional constriction to in the flow increasing frictional expansion losses. It is therefore recommended for the design team that the clearance height be at least the same as the baffle widthspacing. The correlation between pressure coefficient drop and maximum velocity should also be noted. Add the theoretical connection using the pressure drop in an expansion.
Figure 14. Comparison of Turbulent Dissipation Rate for Clearance height of 0.1 m and 0.15 m1b and 1.5b
Figure 14 above further validates that results are not sensitive to the change in clearance height. Contours of turbulence dissipation rate for clearance heights of 0.1 m and 0.15 m 1b and 1.5b were compared. These results show that the region of active turbulent dissipation is the same for both reactors, about two times the length of baffle spacing.
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Figure 16 clearly shows the recirculation region for the three different turbulence models. Since standard K-ε model best represent the flow features seen in the demo plant, it is concluded that standard K-e model best simulate the turn.
4. Conclusions
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- An area of recirculation occurs near the center wall immediately after the turn
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- Pressure coefficient drop over one baffle turn is 3.75
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- After a clearance height of one baffle
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- spacing or greater, the pressure coefficient drop and the maximum velocity becomes constant
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- Most of the energy dissipation occurs in the region after the turn over a distance of about two baffle
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- spacings
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- The pressure coefficient drop is insensitive to the Reynolds number for a large range of inlet velocities
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- A mesh with 20,000 mesh elements is sufficient to obtain accurate results
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- Different turbulence model resulted in fairly different results
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- The standard k-e model best simulates the turn
6. Future Research
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- Measure the Gθ value from FLUENT
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- Analyze the region of very high energy dissipation along the wall near the contraction and explore methods to reduce the energy dissipation in this zone
- Devise improved methods of creating more uniform energy dissipation in the reactor to enhance flocculation efficiency
- Better understanding of different turbulence models
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- Model droplet collision - breakup
7. Acknowledgements
During the course of this project, we received invaluable advice and direction from Prof. Monroe Weber-Shirk, whose leadership of the AguaClara team project spurred this research and technical investigation. All questions we had were directed towards Dr. Rajesh Bhaskaran, his expertise and academic guidance kept us on schedule and on task. We would also like to thank Prof. Brian Kirby for elucidating some technical aspects we encountered. For their help, we are grateful.
References
On the collision of drops in turbulent clouds
P. G. Saffman and J. S. Turner
, Journal of Fluid Mechanics Digital Archive, Volume 1, Issue 01, May 1956, pp 16-30
doi: 10.1017/S0022112056000020, Published online by Cambridge University Press 28 Mar 2006
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