Dead Zone Analysis for Estimating Hydraulic Efficiency in Rectangular Disinfection Chlorine Contactors

Abstract

To increase disinfection potential in a chlorine contactor, it is often recommended to increase the detention time in the contactor, that is, its hydraulic efficiency. This can be accomplished by installing inner devices such as baffle walls, diffuser walls, and intrabasins. To more accurately analyze the effect of such inner devices, it is necessary to conduct transient hydrodynamic analysis, which is computationally intensive. To reduce this computational burden, this study develops a simplified approach using steady-state dead zone analysis. In addition, this study uses the simplified approach to explain, with an indicator of dead zone volume percentage, why hydraulic efficiency changes with using different designs of length/width ratio, shape factor, diffuser walls, and intrabasins. This study suggests a relationship between dead zone volume percentage and hydraulic efficiency to replace length/width ratio. This will increase the estimation accuracy of hydraulic efficiency with various designs of chlorine contactors while avoiding use of computationally intensive transient hydrodynamic analysis.

Introduction

Disinfection in water treatment to inactivate waterborne microorganisms is an important process for public safety. Although integrated disinfection design framework and computational fluid dynamics (CFD) modeling are recently developed for evaluating efficiency of disinfection contactors (Bellamy et al., 2000; Ducoste et al., 2001; Greene et al., 2004), the CT₁₀ value is considered more convenient and practical and has been widely employed for chlorine reactors and ozone towers (Bishop et al., 1993; Cockx et al., 1999; Crozes et al., 1999; Greene et al., 2004; Templeton et al., 2006). The CT₁₀ value is a product of C and T₁₀, where C denotes the concentration of the disinfectant in mg/L and T is the detention time in minutes, in which 10% of fluid passes through a basin (Bishop et al., 1993). The CT₁₀ value should be increased for more effective disinfection. However, increasing the concentration will also increase the potential of forming disinfection byproducts such as trihalomethanes and haloacetic acids. Increasing the size of the contactor leads to increased T₁₀ value. However, in many cases, this is not feasible because of site and budget limitations (Hannoun et al., 1998). As a result, it is usually recommended to increase the hydraulic efficiency of the contactor, which can be accomplished without increasing its size. Among a number of indexes to estimate the hydraulic efficiency, T₁₀/T, where T is a theoretical retention time, is generally used in the field of water treatment (Bishop et al. 1993; Hannoun et al. 1998; Crozes et al. 1999) and has been selected to represent the hydraulic efficiency in the present study.

Hannoun and Boulos (1997), Hannoun et al. (1998), Shilton and Harrison (2003), and Crozes et al. (1999) reported that T₁₀/T was affected by basin shape, inlet and outlet size, and geometry, as well as number and locations of baffle walls, diffuser walls, and intrabasins. The typical shape of a contactor is circular or rectangular. Bishop's research (1993) showed that a circular shape yields a lower T₁₀/T than a rectangular shape. Bishop's (1993) and Crozes' (1999) studies considered only baffle walls and pointed out that the T₁₀/T value generally increased as the number of baffle walls was increased. Here, they introduced an indicator of length/width (L/W) to quantitatively represent the increase of baffle walls, where L is the length of the flow and W the width. Bishop et al. (1993) reported that T₁₀/T linearly increased until the L/W ratio reached ∼20 and approached a limit beyond 20. Crozes' (1999), however, showed that it continuously increased with an increase of the L/W ratio. The maximum efficiencies reported in these studies were 0.7 and 0.9, respectively. This discrepancy appears to be attributable to differences in experimental conditions. Other researchers have examined other factors related to the rectangular basin, including ratio of width to length, and implementation of a diffuser wall and intrabasin. Shin et al. (2006) discussed the effects of shape factor (SF), that is, the ratio of width to length of the rectangular basin, on the basis of a pilot test and mathematical simulation results. They concluded that the larger the SF value was, the higher the hydraulic efficiency became. Also, in previous studies, integration of a diffuser wall and intrabasin, respectively, was reported to increase hydraulic efficiency (Hannoun and Boulos, 1997; Hannoun et al., 1998). Such enhancement of hydraulic efficiency may result from a change of the flow pattern, because baffles, diffuser walls, and intrabasins cause the flow in the contactor to more closely resemble a plug flow.

According to previous studies, generally, low hydraulic efficiency is largely due to short circuits formed in a basin (Lloyd et al., 2003); the addition of devices such as a baffle wall, diffuser wall, and/or intrabasin reduce short circuits, resulting in increased hydraulic efficiency. According to Thackston et al. (1987), the formation of a dead zone causes short circuits and decreases hydraulic efficiency. Hannoun et al. (1998) defined the dead zone as the region where the direction of flow is opposite to that of the main flow. Thackston et al. (1987) defined it as the region where the velocity toward the outlet is considerably less than the average velocity. As such, it is suggested that the degree of elimination of the dead zone according to the installation of such devices determines the increase of hydraulic efficiency. The L/W ratio, which has been used by many researchers including Bishop et al. (1993), Crozes et al. (1999), and Shin et al. (2006), is related to the degree of dead zone formation. However, this ratio cannot be used for contactors with unevenly placed baffle walls, diffuser walls, and intrabasins, cases that are common in the real world (Hannoun et al. 1998).

It is therefore necessary to develop a method to estimate hydraulic efficiency with their use. This can only be accomplished through an analysis of the hydrodynamics induced by their installation. Many researchers analyzed the hydraulic efficiency from transient CFD simulations, which require much efforts (Bishop et al., 1993; Hannoun et al., 1998; Crozes et al., 1999; Shin et al., 2006; Templeton et al., 2006). In this study, we try to simplify the approach by developing a direct relationship between hydraulic efficiency and dead zone volume, which can be obtained by a steady-state CFD simulation. This new approach will be much simpler than the above. The relationship will enable engineers to find the hydraulic efficiency merely by calculating the dead zone volume of a basin with inner devices via a steady CFD simulation.

Materials and Methods

Pilot-scale contactor

In this research, velocity measurement by acoustic Doppler velocimetry (ADV) and estimation of hydraulic efficiency by a tracer test are used to validate the steady and transient CFD simulations, respectively. ADV is one of the technologies used for in situ measurement of three-dimensional velocities. In a pilot-scale contactor having an SF of 0.5 and six baffles, velocity vectors are measured at a depth of 0.2 m by ADV. Readings by ADV are collected 10 times every second at each point for 3 min, and velocity is calculated as an average value in the three-dimensional direction. For validation of the transient simulation, tracer tests in pilot-scale contactors are conducted. As shown in Table 1, two pilot-scale contactors whose SFs are 0.5 and 2, respectively, are used. With different L/W ratios varying from 10 to 50, tracer tests have been conducted. The L/W ratios are increased by installing baffle walls. A flow rate of 77.87 L/min is used with a theoretical detention time of 23.3 min, which corresponds with that used in Crozes' (1999) test. Sodium fluoride (97%), which is chemically stable on reaction, is used as a tracer. The tracer is injected into the basin within 10 s. The standard SPADNS method, which involves the reaction of fluoride with a red zirconium dye solution, was performed for the determination of fluoride concentration (APHA, AWWA, and WPCF, 1985) and it is measured by an LED type spectrophotometer (HS 2300) every 30 s. The hydraulic efficiency is then calculated.

Table 1.

Data of Pilot-Scale Test and Computational Fluid Dynamics Simulation

	SF 0.5	SF 1	SF 2
Geometry of basin (width × length × water level) (m)	1.725 × 3.45 × 0.305	2.44 × 2.44 × 0.305	3.45 × 1.725 × 0.305
Geometry of baffle (width × length × height) (m)	1.42 × 0.01 × 0.305	2.135 × 0.01 × 0.305	3.145 × 0.01 × 0.305
Shape of inlet and outlet		Circular
Radius of inlet and outlet (m)		0.091
Flow rate (L/min)		77.87

SF, shape factor.

Analytical procedure

A CFD simulation is composed of two processes, steady and transient processes. The steady simulation checks the flow pattern only and provides the initial conditions for the transient simulation. In the transient simulation, a tracer is injected into a basin and its movement together with the flow is simulated, thus enabling hydraulic efficiency to be calculated in the CFD model. We adopt the k-ɛ model using the commercial software CFX 5.6. In the CFD model, inlet velocity is assumed to be normal to the inlet surface. The outlet face is specified as the pressure boundary of 1 atm, the same as in Greene's case (2004). The total number of elements varies from 140,000 to 360,000 and smaller elements are assigned in the vicinities of the inlet and outlet to accurately take into consideration their small areas. A no-slip condition at the walls and a free-slip condition at the water surface are assumed. An isothermal condition is used for the simulation.

Three contactor shapes, where the SF is 0.5, 1, and 2, are analyzed with the models to estimate the hydraulic efficiency and dead zone. To analyze the effects of a baffle wall, diffuser wall, and intrabasin on the dead zone, respectively, each contactor is divided into two regions, as shown in Fig. 1: a linear channel region (LCR), designated as , , and , located between baffles, and a turning channel region (TCR), marked as , , and . Diffuser walls are located in the LCR at the end of baffle wall. The diameter of orifices in the diffuser walls is kept at 5 cm. We also place an L-shaped intrabasin in the TCR.

FIG. 1.

Division for dead zone analysis and location of diffuser wall and intrabasin (plane view). (a) SF 0.5, (b) SF 1, and (c) SF 2. SF, shape factor. Color images available online at www.liebertonline.com/ees

For the analysis of the dead zone, we use the ratio of the dead zone volume to the contactor volume, called the dead zone volume percentage (DVP), as follows: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} \begin{align*} {\rm DVP} \ (\%) = \frac {Dead\ zone\ volume} {Contactor\ volume} \times 100 \tag {1} \end{align*} \end{document}

As there are two definitions of the dead zone, as discussed above, and it is not known which is more appropriate for the present analysis, two ratios were first evaluated. DVP_H is a DVP calculated with the definition given by Hannoun et al. (1998). DVP_T uses a modified definition given by Thackston et al. (1987), stating that the dead zone is a region where the velocity toward the outlet is less than 10% of the average velocity of each channel in the contactor. To calculate DVP_H and DVP_T, post–post processing work is carried out as follows:

In case of DVP_T, average velocity in each LCR and TCR should be calculated by dividing flow rate to cross-sectional area of the region.

Because main flow direction is different in each region, elements' volume of defined dead zone should be obtained in each LCR and TCR. For example, the main flow direction of odd-numbered LCRs such as , , and in Fig. 1a is right. So, in case of DVP_H, dead zone is calculated by elements' volume presenting left direction of flow. In case of DVP_T, dead zone in each region is calculated by deriving the elements' volume in which right direction velocity is less than 10% of average velocity.

Consequently, overall dead zone volume of a contactor could be calculated by adding up dead zone volume of each region. DVP_H and DVP_T can be derived by dividing each overall dead zone volume by the contactor's volume.

Results and Discussion

Validation of CFD model

For validation of the steady CFD model, the velocity map presented in Fig. 2 is used. In Fig. 2, the left side shows the measured flow map and the right the simulated flow. As shown here, there is a large vortex in all LCRs of both cases, creating a dead zone in each LCR. This agrees precisely with in the findings of Wang and Falconer (1998), who noted that the standard k-ɛ turbulence model is the most accurate means of describing the flow pattern in contactor. In each channel for both cases, the velocity at the right-hand side is higher than that of the other side. Flow in TCR turns toward the outlet but is not uniform in both the ADV measurement and the CFD simulation. Measured velocity is compared with the simulated one in terms of magnitude and direction for the quantitative analysis as shown in Fig. 3. The measured velocities of 15 samples in the fifth LCR correlated with those of steady simulation. The result shows that the correlation of magnitude is worse than that of direction. Potentially, this results from different variations of the velocity direction and magnitude according to estimation points. That is, because regular pattern of velocity direction such as the vortex is observed as previously mentioned, the difference between measured and simulated velocity direction is not high irrespective of small difference of estimation points but the magnitude difference can be high because the small difference of estimation points makes a relatively large variation of velocity's magnitude. However, because the difference between measured and simulated velocity is not high and determination coefficient (R²) of magnitude and angle is 0.825 and 0.894, respectively, we can conclude that the steady CFD model depicts the actual flows in a contactor accurately enough for analysis.

FIG. 2.

Velocity estimation in a pilot-scale contactor by (a) acoustic Doppler velocimetry measurement and (b) computational fluid dynamics simulation.

FIG. 3.

Comparison of measured and simulated velocity with respect to (a) magnitude and (b) direction.

For validation of the transient CFD model, nine trace tests are conducted in pilot basins, whose SF is 0.5 and 2. As shown in Fig. 4, comparing measured hydraulic efficiencies with simulated ones, a high correlation is shown with an R² value of 0.89. Because, generally, R² > 0.8 is acceptable for validating CFD model (Thackston et al., 1987; Shin et al., 2006; Yum et al., 2008; Theodoropoulos and Deligiorgis, 2009), we conclude that the developed transient CFD model reflects the flow pattern and hydraulic efficiency in the contactor reasonably well.

FIG. 4.

Comparison of tracer-tested and computational fluid dynamics-simulated hydraulic efficiencies.

Effect of baffle walls and basin shape on dead zone and hydraulic efficiency

A total of 18 cases were simulated with the validated models, whose data and results are shown in Table 2. Their hydraulic efficiencies are plotted with respect to L/W ratio in Fig. 5. As is already well known, the efficiency becomes higher as the ratio increases (Bishop et al., 1993; Crozes et al., 1999). However, hydraulic efficiency gradually approaches an asymptotic value as the L/W ratio increases. The asymptotic value differs with the SF, like in Shin's research (2006). Figure 5 shows that the ratio is about 0.6 for an SF of 0.5, 0.63 for SF 1, and 0.73 for SF 2. This result is much similar to the Bishop's curve (1993), showing that it was around 0.7. However, the Clark's curve (1999) does not clearly show the same pattern, that is, no asymptotic line. We believe that it may be partly due to that the curve was drawn without having an asymptotic line in mind.

FIG. 5.

Hydraulic efficiencies with L/W ratio. L/W, length/width.

Table 2.

Estimation of Hydraulic Efficiency and Dead Zone Volume Percentages with Length/Width Ratio

			DVP_H (%)			DVP_T (%)
Baffle wall		L/W ratio	TCR	LCR	Total	TCR	LCR	Total	T₁₀/T
SF 0.5	4	12.65	10.4	36.8	47.2	12.2	38.2	50.4	0.40
	5	18.26	11.4	33.3	44.7	13.3	35.1	48.4	0.44
	6	24.93	11.5	33.3	44.8	14.3	35.0	49.3	0.48
	7	32.66	10.9	30.1	41.0	13.4	31.3	44.7	0.54
	8	41.46	10.8	28.7	39.4	13.2	30.0	43.2	0.56
	9	51.34	10.8	28.3	39.1	13.3	29.0	42.3	0.58
	10	62.31	9.5	29.3	38.8	13.4	30.7	44.1	0.59
SF 1	2	9.07	5.8	44.8	50.5	7.1	46.2	53.3	0.41
	3	16.20	5.4	38.4	43.8	6.9	40.7	47.6	0.48
	4	25.41	6.0	33.9	39.9	7.8	36.0	43.8	0.51
	5	36.75	5.4	32.8	38.3	7.9	34.7	42.6	0.57
	6	50.23	5.9	31.3	37.2	8.3	33.4	41.7	0.61
	7	65.89	5.0	23.9	28.9	8.1	26.0	34.2	0.63
SF 2	1	8.04	0.6	46.0	46.6	1.7	47.6	49.2	0.40
	2	18.21	1.8	37.6	39.4	3.2	40.3	43.5	0.59
	3	32.57	1.7	24.0	25.7	3.9	26.8	30.6	0.70
	4	51.19	1.6	19.8	21.4	3.0	21.9	24.8	0.73
	5	74.15	1.8	18.7	20.5	3.8	20.4	24.2	0.72

DVP, dead zone volume percentage; LCR, linear channel region; L/W, length/width; TCR, turning channel region.

At the same L/W ratio, hydraulic efficiency differs according to the SF value. That is, the larger the SF value is, the higher the hydraulic efficiency is. This indicates that the basin shape itself becomes an important factor to affect hydraulic efficiency. This result agrees with Shin's research (2006). These observations indicate that hydraulic efficiency in a contactor cannot be explained with L/W ratio alone. The basin shape is another factor that should be considered.

Dead zone analysis is shown in Table 2 in terms of DVP_H and DVP_T. Here, all index values are obtained using the steady simulation results only. The hydraulic efficiency, T₁₀/T, is a result of the transient simulation. As more baffles are installed in a basin, the dead zone in the LCR decreases, whereas that in the TCR remains nearly unchanged, as shown in Fig. 6. Therefore, the increase of hydraulic efficiency with larger L/W ratios can be attributed to the decrease of the dead zone in the LCR. That is, when the L/W ratio increases from 12.65 to 62.31 in the case of SF 0.5, DVP_H in the LCR decreases from 36% to 29%. In the case of SF 1 and 2, it changes from 44% and 45% to 23% and 18%, respectively, as the L/W ratio increases. However, in the cases of SF 0.5, 1, and 2, even when the L/W ratio increases, the dead zone in the TCR remains at 10%, 5%, and 1.5%, respectively. In the cases of DVP_T, although there is slight variation in the actual values, the tendency is the same. Because dead zone largely tends to occur in area behind baffles (Thackston et al., 1987; Kim et al., 2010), DVPs of LCR is much greater than that of TCR and eddy flow was not observed in the TCR bent by 180° except corners, like in previous researches (Wang and Falconer, 1998; Kim et al., 2010). Potentially, this is because the TCR has not enough rooms for forming eddy flow comparing with the LCR and outer flow in the TCR is stronger than inner flow (Blanckaert and Graf, 2001). Relatively, the narrow cross section in TCR makes flow to have same direction. Moreover, the fast outer flow in bending flow of the TCR gets main flow in the LCR toward outlet to form in areas far from baffles and dead zone to occur behind the baffles.

FIG. 6.

Variation of DVP_H in LCR and TCR with respect to L/W ratio. DVP, dead zone volume percentage. LCR, linear channel region; TCR, turning channel region.

This analysis of the dead zone reveals why the hydraulic efficiency differs with SF. Figure 7 shows the TCR volume percentage with respect to L/W ratio. As shown, a contactor with a higher SF value has smaller TCR volume percentages at the same L/W ratios. That is, the contactor has larger LCR volume percentages. As the DVP in the LCR only decreases with an increase of L/W ratio, as discussed above, this further indicates that the higher the SF value becomes, the higher the hydraulic efficiency of the contactor at a same L/W ratio.

FIG. 7.

TCR volume percentages to L/W ratio.

This dead zone analysis again explains why the hydraulic efficiency approaches an asymptotic value at each SF value as the L/W ratio increases. Specifically, as shown in Fig. 7, as the L/W ratio increases, the TCR volume percentage asymptotically increases and the DVP ratio in the TCR remains almost the same. That is, regardless of how many baffles are installed, the TCR in a basin and the DVP in the TCR cannot be reduced beyond a certain limit. As a result, hydraulic efficiency approaches values of 0.6, 0.63, and 0.73 in basins with SF values of 0.5, 1, and 2, respectively.

Effect of diffuser wall and intrabasin on DVP and hydraulic efficiency

To analyze the effects of diffuser walls and an intrabasin on the dead zone and hydraulic efficiency, a total of 24 cases were simulated and the results are shown in Table 3. There are eight groups, where each has the same SF value and baffle walls. Each group consists of three cases: a default case with baffle walls only and the cases with diffuser walls and intrabasins, respectively. As SF value, L/W ratio, and the use of a diffuser wall or intrabasin are factors that differentiate each case, the groups were established to evaluate the effects of them.

Table 3.

Estimation of Hydraulic Efficiency and Dead Zone Volume Percentages with Diffuser Wall and Intrabasin

				DVP_H (%)			DVP_T (%)
Shape Factor	Baffle walls	Additional innerdevices	L/W ratio	TCR	LCR	Total	TCR	LCR	Total	T₁₀/T
SF 0.5	5	—	18.26	11.4	33.3	44.7	13.3	35.1	48.4	0.44
		Diffuser wall		6.8	20.4	27.2	9.9	22.6	32.5	0.62
		Intrabasin		10.0	24.6	34.6	12.9	26.1	38.9	0.61
	10	—	62.31	9.5	29.3	38.8	13.4	30.7	44.1	0.59
		Diffuser wall		6.8	15.8	22.6	10.8	17.6	28.5	0.73
		Intrabasin		11.0	12.8	23.8	14.5	14.0	28.5	0.75
SF 1	2	—	9.07	5.8	44.8	50.5	7.1	46.2	53.3	0.41
		Diffuser wall		4.0	29.2	33.3	5.8	31.7	37.5	0.49
		Intrabasin		5.2	35.8	41.0	6.8	36.4	43.2	0.46
	3	—	16.20	5.4	38.4	43.8	6.9	40.7	47.6	0.48
		Diffuser wall		3.0	21.0	23.9	5.3	23.2	28.5	0.65
		Intrabasin		5.1	25.8	30.9	6.9	27.5	34.4	0.58
	6	—	50.24	5.9	31.3	37.2	8.3	33.4	41.7	0.61
		Diffuser wall		3.1	14.4	17.5	5.7	15.5	21.2	0.71
		Intrabasin		6.2	13.0	19.2	9.0	14.1	23.1	0.74
SF 2	1	—	8.04	0.6	46.0	46.6	1.7	47.6	49.2	0.40
		Diffuser wall		0.7	39.8	40.6	1.8	43.2	45.0	0.51
		Intrabasin		0.9	34.0	34.9	1.7	36.1	37.8	0.45
	2	—	10.35	1.8	37.6	39.4	3.2	40.3	43.5	0.59
		Diffuser wall		2.6	28.3	30.9	4.0	23.7	27.7	0.63
		Intrabasin		2.9	20.7	23.6	4.4	22.4	26.8	0.68
	5	—	74.15	1.8	18.7	20.5	3.8	20.4	24.2	0.72
		Diffuser wall		2.3	13.0	15.3	4.3	14.1	18.3	0.75
		Intrabasin		5.1	10.7	15.8	6.7	11.3	18.0	0.77

The simulation results shown in terms of DVPs and hydraulic efficiency indicate that the use of a diffuser wall or intrabasin increases the hydraulic efficiency more than the use of a baffle wall only (Hannoun and Boulos, 1997; Hannoun et al., 1998). In the case where SF value is 0.5 with five baffles, that is, the L/W ratio is 18.26, the DVP_H in the LCR reduces from 33.3% to 20.4% and 24.6% with implementation of a diffuser wall and intrabasin, respectively, whereas the DVP_T decreases from 35.1% to 22.6% and 26.1% for the same cases. These effects are also presented in other cases with different SF values and L/W ratios.

The dead zone in the TCR is different from that in the LCR. That is, the use of a diffuser wall and intrabasin does not always reduce the DVPs in the TCR. Rather, their use increases the DVPs slightly. Because dead zone can easily occur by obstructions (Thackston et al., 1987), we believe that a new dead zone in the TCR is created by the diffuser wall and intrabasin. Regardless of the mechanism, it is shown that their use reduces the overall dead zone in all cases and thus increases hydraulic efficiency.

Figure 8 shows the effects of the addition of a diffuser wall and intrabasin, indicating that roughly 42% DVP_H is a threshold to distinguish between the effect of intrabasin and that of diffuser wall. The y-axis presents the relative hydraulic efficiency, which is the ratio of hydraulic efficiency of the cases with an additional device to that of the default case in each group. Given that all the ratios are larger than 1.0, it is concluded that the addition of these features improves the hydraulic efficiency. This agrees with previous researches (Hannoun and Boulos, 1997; Hannoun et al., 1998). In Fig. 8a, the ratios of each group are shown in terms of DVP_H. Interestingly, when DVP_H is smaller than 42%, the addition of an intrabasin yields higher ratios, and when it is larger than 42%, the addition of a diffuser wall provides higher ratios. This indicates that implementation of a diffuser wall together with a baffle wall is more effective in terms of hydraulic efficiency in the case of a higher DVP_H than the use of an intrabasin, and vice versa in the case of a lower DVP_H. The dividing line for these trends is roughly 42%. Because additional devices such as diffuser walls and intrabasins have an effect on the decrease of DVPs in the LCR, diffuser walls are more helpful to decrease DVPs in the LCR in a high dead zone volume.

FIG. 8.

Comparison of effects of diffuser wall and intrabasin with DVP_H (a) and L/W ratio (b).

As shown in Fig. 8b, we evaluated whether the same tendency could be observed with L/W ratio. With one exception, there is a similar tendency; that is, in cases with higher L/W ratio, the intrabasin works better with a baffle wall than a diffuser wall and vice versa at a lower L/W ratio. The exception is the case of SF 2 with two baffles. This suggests that when there are additional devices such as a diffuser wall and intrabasin, the DVP is better for determining an additional device than the L/W ratio.

Estimating hydraulic efficiency with DVP

To more accurately estimate the hydraulic efficiency of a contactor in the real world, it is necessary to consider many factors such as the basin shape, baffle wall, diffuser wall, and intrabasin. As an attempt to develop such an approach, we plotted together the results as shown in Fig. 9. That is, we attempted to relate the hydraulic efficiency to DVP. Figure 9 shows their relationships with R² values of 0.850 and 0.815, respectively, with a 95% significance level and p-values of <0.0001. Although good relationships were derived, DVP_H always resulted in higher R² values, indicating that it is a better index than DVP_T. That is, the dead zone, defined as the region where the direction of velocity is opposite to that of the main flow, works better with the hydraulic efficiency in a contactor. Also, from the plot in Fig. 9, the following equation has been derived: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6} \begin{document} \begin{align*} Hydraulic\ efficiency = \frac{T_{10}} {T} = \frac{0.9466}{1 + \exp (( {\rm DVP}\_{\rm H} (\%) - 43.98) / 20.53)}\tag{2} \end{align*} \end{document}

FIG. 9.

Relationship between DVP and hydraulic efficiency.

This equation suggests that hydraulic efficiency can be calculated by finding a DVP from a steady CFD simulation. As a transient simulation and a wet test with a tracer are not necessary to estimate the hydraulic efficiency of a contactor, regardless of its shape or incorporated devices, this equation will be helpful in designing a new contactor and estimating the efficiency of exiting contactors. Using only a steady simulation, this analysis enables engineers to save computational time and costs. In addition, the equation dictates that the maximum hydraulic efficiency cannot be greater than 0.847 regardless of basin shape and additional inner devices when DVP_H is zero. However, because it is hard to make ideal plug flow and dead zone will inevitably form, we conclude that it is difficult to obtain T₁₀/T that exceeds 0.80 (±0.5 95% confidence interval).

As this work focuses on the effect of additional devices such as baffles, diffuser walls, and intrabasins in various shapes and was done under the same flow rate and water depth, simulations and wet tests under various flow rates and water depths might be needed to apply this relationship in a real-world contactor. In further study, considering these operating parameters (i.e., flow rate and water depth) will be studied and it will turn out that this relationship can be applied in a real contactor.

Conclusions

In this research, hydraulic efficiency was estimated by dead zone analysis in a chlorine contactor where inner devices such as baffle wall, diffuser wall, and intrabasin were installed. Previous researches focused only on hydraulic efficiency based on transient CFD simulation and tracer tests (Bishop et al., 1993; Hannoun et al., 1998; Crozes et al., 1999; Shin et al., 2006; Templeton et al., 2006). However, this research reveals the direct relationship between hydraulic efficiency (i.e., T₁₀/T) of contactors and hydrodynamics based on steady CFD simulation. This analysis is helpful to decrease the computational load and engineers' efforts by simplifying CFD simulation. The results are summarized as follows:

The hydraulic efficiency increase asymptotically as the L/W ratio and SF value increase. A dead zone analysis with a CFD simulation indicates that this is due to the DVP in the LCR being continuously reduced and the DVP in the TCR remaining almost unchanged. Their asymptotic values increase as their SF values increase. The dead zone analysis explains that this increase in the asymptotic values is due to the increase of LCR volume, in which DVP can be reduced, as the SF values become larger.

The effects of a diffuser wall and intrabasin in a contactor on the hydraulic efficiency were estimated well by the dead zone analysis. The dead zone analysis results show that installing a diffuser wall or intrabasin together with a baffle wall can further increase the hydraulic efficiency by reducing the DVP further. In coupled use with baffle walls, a diffuser wall is more efficient in increasing the hydraulic efficiency than an intrabasin when DVP_H is higher than 42%.

A regression equation was derived to relate the hydraulic efficiency to DVP_H. This equation provides a simple method in predicting contactor hydraulic efficiency based on steady CFD simulation results. However, it should be noted that this equation is based on a limited number of the pilot tests. The impacts of some important factors, such as flow rate and water depth, have not considered in this equation. Further studies need to be done to evaluate these factors and improve this equation to apply it in the design of real-world contactors.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

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