Two-phase flow simulation of reactor clarifiers

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Journal of the Chinese Institute of Chemical Engineers 39 (2008) 275–280 www.elsevier.com/locate/jcice

Short communication

Two-phase flow simulation of reactor clarifiers Wen-Jie Yang, Chu-Chuao Wang, Ren-Yi Hsu, Rome-Ming Wu * Department of Chemical and Materials Engineering, Tamkang University, Tamsui, Taipei County 251, Taiwan Received 4 September 2007; accepted 7 January 2008

Abstract In this work, hydrodynamic behavior of flow in three different reactor clarifiers was simulated by three-dimensional, multiphase flow model. The primary construction of reactor clarifier was based on the Bansin Water Treatment Plant, Taiwan. This is the traditional construction, and we call it Type A. The other two were designed in such a way as to improve effluent water quality. The traditional clarifier construction was varied in these to make a large well angle (Type B) and a gradually larger inlet pipe (Type C). Solid effluent flux can be calculated directly from this model. The simulation results showed that under the same daily throughput, the Type C construction of clarifier could decrease upflow fluid velocity in the clarifier and, therefore, reduce effluent water turbidity. # 2008 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Multiphase; CFD; Clarifier; Turbidity

1. Introduction A reactor clarifier that recirculates sludge is very economical and compact, having two principal functions—coagulation/ flocculation and sedimentation (Crittenden et al., 2005). Coagulation, the chemistry-based treatment stage, controls the characteristics of the generated sludge layer, whereas sedimentation, which is the hydrodynamic treatment stage, controls sludge layer stability. Therefore, the existence and recirculation of a sludge layer in a clarifier is essential to produce quality potable water. Since the 1990’s, Taiwan Water Supply Corporation (TWSC) has installed reactor clarifiers for treating drinking water (Lin et al., 2004; Sung et al., 2003, 2005a). Reactor clarifiers supply over 50% of the drinking water to Taiwan’s public. The stability of the sludge blanket is controlled by the settling and upflow velocity of the coagulated flocs (Annadurai et al., 2002; Head et al., 1997; Sung et al., 2005b). Takacs et al. (1991) used solids flux theory and mass balance to predict the solid profile of the clarification-thickening process. The one-dimensional settler was divided into 10 sublayers, and it suggested a double exponential expression representing the settling function. Wett (2002) also used solids

* Corresponding author. Tel.: +886 2 26215656x3286; fax: +886 2 26209887. E-mail address: [email protected] (R.-M. Wu).

flux theory to interpret a three-layer (clarification, hindered settling, and compression zone) sedimentation model. Ekama and Marais (2004) gave a survey of the development of 1-D settler modeling. Generally speaking, solids flux theory is commonly applied and is suitable for predicting the solid concentration in a settling tank. In order to describe solid effluent concentration and hydraulic effect in a reactor clarifier, however, a two-phase 3-D modeling flow pattern is needed. Besides using solids flux theory, some studies have tried to link an experimental index with the performance of the clarifier. Vanderhasselt and Vanrolleghem (2000) linked sludge volume index through empirical functions by a dilution experiment. Giokas et al. (2003) used sludge volume index to compare measurements and predict zone settling velocity parameters. There have been some studies which have simulated the performance of a clarifier by CFD. Lee (2005) and Wu et al. (2007) simulated the flow pattern of a clarifier with a porous medium as a sludge blanket via 3-D CFD. Their works were not based on solids flux theory or sludge volume index, etc., but tried to directly solve the three-dimensional flow field in a blanket clarifier using computational fluid dynamics. To our knowledge, Wu et al. (2008) was the first work to utilize a 3D, multiphase flow simulation for a clarifier. This study attempts to improve effluent water quality of a clarifier by altering its geometric construction. The simulation is based on the sludge blanket clarifier established at the Bansin Water Treatment Plant, Taiwan.

0368-1653/$ – see front matter # 2008 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jcice.2008.01.002

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Nomenclature Aout CD ds D f ~ g m ˙ m ˙ 00 m ˙ out p ~ R Res vi ~ v v0s V

outflow surface (m2) drag coefficient diameter of particle (m) interphase momentum exchange coefficient correlation factor acceleration of gravity (m/s2) mass flow rate (kg/m3 s) solid effluent flux (kg/m2 s) outflow solid mass flow rate (kg/s) pressure (N/m2) water/solid interaction (N/m2) Reynolds number inlet velocity (m/s) water/solid velocity (m/s) terminal velocity correlation volume of each phase (m3)

Greek symbols a volume fraction ai initial solid volume fraction l bulk viscosity (kg/m s) m shear viscosity (kg/m s) r density (kg/m3) rˆ effective density (kg/m3) t˜ stress tensor (N/m2) ts particulate relaxation time (s) vi impeller rotation speed (rad/s)

tions. Note that the horizontal black line is the top plate of the clarifier, while the blue line indicates the water surface (a do not-like surface). Fig. 1(c) displays Type C, a gradually larger inlet pipe construction. Fig. 2 shows the corresponding calculation meshes. 3. Governing equations and boundary conditions 3.1. Eulerian multiphase flow The volume of phase j, Vj, is defined by: Z a j dV; Vj ¼

(1)

V

where aP j is phase volume fraction occupied by each phase, n hence j¼1 a j ¼ 1. The effective density of phase j is rˆ j ¼ a j r j , where rj is the density of phase j. The continuity equation for phase j is: @ ðrˆ Þ þ r  ðrˆ j~ v j Þ ¼ 0; @t j

(2)

where ~ v j is the velocity of phase j. The momentum balance for phase j yields: @ ðrˆ ~ v j Þ þ r  ðrˆ j~ v j~ v jÞ @t j gþ ¼ a j r p þ r  t˜ j þ rˆ j~

n X

ð~ Rk j þ m vk j Þ ˙ k j~

(3)

k¼1

Subscripts s solid phase w water phase

The Bansin Water Treatment Plant is in Banchiao City, Taipei County, Taiwan. It takes raw water from Yuanshanyan (Yuanshan weir) and Shihmen Reservoir at a rate of about 1,200,000 m3 per day with polyaluminum chloride (PACl) as the coagulant. The sludge blanket is noted as rather unstable (Chen et al., 2003). About every 20 min the sludge blanket overturns somewhere and solid flux of the effluent increases, creating a large load on the following sand filtration. 2. Geometry and meshes Fig. 1(a) indicates the geometry of the reactor clarifier (Type B, large well angle). The clarifier is of size 19 m  19 m  5.5 m, with a 16 blades and impellers of 3.2 m in diameter at the center and at the top of the clarifier. The inlet pipe is 0.9 m in diameter and usually has an inlet water velocity of 0.34 m/s. The inlet pipe is connected to a 2.4 m diameter draft tube, which is the first reaction zone. The second reaction zone is outside reaction zone 1 and inside a cone well with upper and lower diameters 8 and 16 m and a height of 3.8 m, respectively. Fig. 1(b) shows construction of Type A (the traditional construction) and water surface boundary condi-

where ~ Rk j is an interaction force between phases, p is the pressure shared by all phases, and ~ vk j ¼ ~ v jk is the interphase velocity. If m ˙ k j > 0 (i.e., phase k mass is being transferred to phase j), ~ vk j ¼ ~ vk . If m vk j ¼ ~ v j . Here t˜ j is the jth phase ˙ k j < 0, ~ stress–strain tensor and defined as follows:  t˜ j ¼ a j m j

vTj r~ v j þ r~



   2 þ a j l j  m j r  r~ v j I˜ ; 3

(4)

where mj and lj are the shear and bulk viscosity of phase j. 3.2. Interaction force ~ Rk j depends on the friction, pressure, cohesion, and other effects, and is subject to the conditions where ~ Rk j ¼ ~ R jk and ~ R j j ¼ 0. The interaction term is of the following form: n n X X ~ Rk j ¼ Dk j ð~ vk  ~ v j Þ; k¼1

(5)

k¼1

where Dkj (=Djk) is the interphase momentum exchange coefficient. The water–solid exchange coefficient Dsw can be written in the following general form: Dsw ¼

as rs f ; ts

(6)

W.-J. Yang et al. / Journal of the Chinese Institute of Chemical Engineers 39 (2008) 275–280

Fig. 1. Geometry of the clarifier. (a) Type B; (b) Type A; (c) Type C.

Fig. 2. Meshes of the clarifier.

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where ts is the particulate relaxation time and is defined as ts ¼

rs ds2 ; 18ml

(7)

where ds is the diameter of particles of solid phase s. For the Syamlal and O’Brien (1989), f can be defined as f ¼

CD Res aw ; 24v0s 2

(8)

where the drag function has the form:  2 4:8 C D ¼ 0:63 þ pffiffiffiffiffiffiffiffiffiffiffiffiffi ; Res =v0s Res ¼

rs ds j~ vs  ~ vw j ; mw

(9) (10)

where v0s is the terminal velocity correlation for the solid phase (Garside and Al-Dibouni, 1977):  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v0s ¼ 0:5 A 0:06Res þ ð0:06Res Þ2þ 0:12Res ð2B  AÞþ A2 ; (11) 2:65 with A ¼ a4:14 w , and B ¼ aw , for aw > 0.85. The boundary conditions are as follows:

~ vw ¼ ~ vs ¼ constant; p ¼ 0;

@water surface

as ¼ 0:05; as ¼ 0:5;

@inlet pipe

@inlet pipe 8 < 9:5 m < x < 9:5 m @ 9:5 m < y < 9:5 m : 0m
(12a) (12b) (12c) (12d)

Eq. (12a) states that the inlet suspension (water and solids) is moving at a constant speed. Eq. (12b) describes the fact that the gauge pressure at the water surface (top of the clarifier, Fig. 1(b) is zero. Eq. (12c) states that the inlet suspension has a solid volume fraction of 0.05. At the bottom of the clarifier, there is assumed to be a homogeneous sludge blanket of solid volume fraction 0.5. Eq. (12d) interprets this situation. The computational fluid dynamics program FLUENT 6.1 (Fluent Inc., U.S.A.) solved the governing equations, Eqs. (2) and (3), together with the associated boundary conditions Eqs. (12a)–(12d), using hybrid mesh volumes. There are about 2,500,000 mesh volumes. The calculations were carried out with maximum relative error of 104 in fluid velocity evaluation. The maximum relative errors for upflow velocity at elevation z = 2.2 m are less than 5% when compared with TWSC. 4. Results and discussion 4.1. Velocity vector of water flow Fig. 3 plots the velocity vector of fluid mixture in the clarifier (inlet velocity = 0.3 m/s; impeller rotation speed = 0.9 rad/s).

When inlet water flows into the draft tube, it is sucked to the top of the clarifier by the rotating impeller. Then, it goes down along well inside and separates into two streams. One stream inside the well makes a strong cycling flow (C1) in the reaction well, and the other stream rises along the clarifier wall to the effluent surface, and descends along the reaction well outside, making a relatively weaker cycling flow (C2). We suggest that flocs may be hydrodynamically elutriated by the cycling flow C2, leading to a 20-min overturn on average, as reported by Chen et al. (2003). Conventional thinking is to coagulate the flocs into a strong, dense blanket. 4.2. Solid volume fraction Fig. 4 reveal the contours of volume fraction of solid phase over time. The primary phase is the water phase; the secondary phase is the solid phase with uniform particle size 10 mm and density 1005 kg/m3. As time evolves, solid particles were sucked from the draft tube to the top of the impeller, then descended from the reaction well inside, filled the whole reaction well, and overflowed into the reaction well outside, making a relatively stable blanket at the bottom of the clarifier, and a dynamic upward particles/water boundary surface. Comparing Fig. 4(a)–(c), it is obviously shown that, as time evolves, the boundary surface of particles/water becomes high, i.e., a large quantity of particles rise and the loading of the following fast filtration becomes heavy. In order to enunciate the construction effects on the stability of the sludge blanket, the other two constructions of clarifiers were studied. One is the larger reaction well angle (1368, Fig. 4(d)–(f), the original angle being 1208), another is the gradually larger inlet pipe (From inlet entrance to draft tube entrance, there is a 1.6-fold increase in pipe diameter (Fig. 4(g)–(i). Comparing the particle/water surface boundary with these figures, it is shown that after 3600 s operation, the lowest particles/water surface boundary happens at the Type C construction, the gradually larger inlet pipe. 4.3. Solid effluent flux From this two-phase, 3-D simulation method, the solid effluent flux could be evaluated directly. This is shown as the mass flow rate of solids flow out the clarifier ðm ˙ out Þ divided by the outflow surface (Aout). The following equation is the definition of solid effluent flux m ˙ 00 : m ˙ 00 ¼

m ˙ out Aout

(13)

Fig. 5 depicts the effects of impeller rotation speed on solid effluent flux of the Type A clarifier. High rotation speed causes particles circulating in the reaction well to be under intensely strong centrifugal force. This intense circulating then brings on high upflow velocity outside the reaction well, resulting in high solid effluent flux. Fig. 6 displays effects of inlet solid concentrations on solid effluent flux of Type A clarifier. The inlet solid concentration is that inlet solid volume fraction ai equal to 0.05, 0.005, and

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Fig. 3. Velocity vector of water flows (inlet velocity vi ¼ 0:3 m=s, impeller rotation speed v = 0.9 rad/s).

Fig. 4. Contour of solid volume fraction in clarifier (vi ¼ 0:3 m=s, v = 0.9 rad/s). (a) Type A, t = 1200 s; (b) Type A, t = 2400 s; (c) Type A, t = 3600 s; (d) Type B, t = 1200 s; (e) Type B, t = 2400 s; (f) Type B, t = 3600 s; (g) Type C, t = 1200 s; (h) Type C, t = 2400 s; (i) Type C, t = 3600 s.

Fig. 5. Solid effluent flux of Type A clarifier under different impeller rotation speeds (vi ¼ 0:3 m=s, ai = 0.05).

Fig. 6. Solid effluent flux of Type A clarifier under different inlet solid volume fractions (vi ¼ 0:3 m=s, v = 0.9 rad/s).

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Acknowledgement The authors would like to acknowledge the financial support received from the National Science Council of Republic of China.

References

Fig. 7. Solid effluent flux of three constructions of clarifiers (vi ¼ 0:3 m=s, ai = 0.05, v = 0.9 rad/s).

0.00005, respectively. It is obvious that, during the early 2500 s of operation, a diluted inlet solid concentration leads to a low solid effluent flux. After 2500–3600 s, solid effluent flux converges to about 0.1 kg/m2 s. Remember that the inlet to the clarifier is the outlet from the previous solid/liquid separation unit, say, the sedimentation tank. Therefore, from this simulation, it seems there is little effect of the upstream solid concentration on the clarifier solid effluent flux. In order to highlight the differences between the three constructions, the effluent solid flux is displayed in Fig. 7. For Type A and Type B, the first 2500 s of operation is stable. After that, the solid effluent flux increases dramatically. For Type C, the stable/unstable boundary appears at 2000 s. Just before 3000 s of operation, the solid effluent flux is the lowest in the Type C construction. After 3000 s, the solid effluent flux of Type C is higher than that in Type A. 5. Conclusions Blanket floc volumetric concentration is an important parameter in understanding the performance of reactor clarifiers. Two-phase, 3-D simulations of a clarifier using three different constructions were studied in this work. Solid effluent flux can be calculated simply via this simulation method. From the results of the solid effluent flux, it is suggested that, under the same daily throughput, the gradually larger inlet pipe can reduce the solid effluent flux and produce better quality water at about 3000 s operation. According to the simulation results, drainage of sludge at every 3000 s is needed. It is recommended that TWSC considers making gradually larger inlet pipes to obtain better quality water under the same daily throughput, or the same quality water with larger daily throughput.

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