The impact of turbulence models on the simulation of residence time distribution in a multichamber ozone contactor Open Access

Ozone disinfection plays an important role in the advanced treatment of drinking water because of its strong disinfection effect, high disinfection efficiency, and wide range of sterilization (Helen et al. 2003; Lee et al. 2015; Verma et al. 2016; Kolosov et al. 2018). However, bromate, which is a potential carcinogen (group 2B), may be produced when water contains bromide ions (Kim et al. 2007). Therefore, it is very important to control the formation of bromate in the ozone disinfection process. The amount of bromate produced in ozone disinfection process can be affected by ozone dosage, reaction time, ozone distribution, reaction temperature, and concentration of bromide ion. To control the bromate production and improve the disinfection efficiency, the hydrodynamics, raw water quality and operating conditions should be carefully determined during ozone disinfection.

Residence time distribution has been widely used to evaluate the hydrodynamics in ozone contactors (Wilson & Venayagamoorthy 2010). Commonly used values are ⁠, ⁠, ⁠, representing the ratio of the time for 10, 50 and 90% of inlet tracer flowing out of the ozone contactor, respectively (Ender & Mustafa 2018). In addition, the Morrill dispersion index (MDI), which is defined as the ratio of the characteristic residence time to ⁠, is used to evaluate the relationship between the mixing level of the fluid and the relative distribution of the tracer between and in the ozone contactor. Recently, a new parameter, namely recirculation factor, was presented to characterize the contact tank, which is defined as the difference between unity and the ratio of the volume occupied by the recirculation zones and the overall volume of the reactor (Bruno et al. 2021). These parameters can be obtained by the tracer experiment (Martin et al. 1992; Wols et al. 2008; Kim et al. 2010a) and computational fluid dynamics (CFD) (Choi et al. 2004; Zhang et al. 2007, 2014a; Talvy et al. 2011; Zou et al. 2017; Aparicio-Mauricio et al. 2020). Contact tank geometry has a significant effect on the mixing efficiency. Slot-baffled and perforated baffled contact tank have been developed to improve the mixing efficiency and optimize disinfection treatment (Aral & Demirel 2017; Demirel & Aral 2018a; Bruno et al. 2020, 2021).

Flow in ozone contactors is usually turbulent. The simulation of turbulence plays an important role in the prediction of residence time distribution. Large-eddy simulation (LES) is viewed as a powerful tool in the simulation of ozone contactors (Wang & Falconer 1998; Kim et al. 2010b, 2013; Zhang et al. 2013a, 2013b, 2014b; Demirel & Aral 2016). Wang & Falconer (1998) investigated residence time distribution using and LES. The peak time was mainly influenced by the advection effect. Kim et al. (2010b, 2013) conducted by a three-dimensional numerical simulation of flow and tracer transport in a multichamber ozone contactor using LES. It was concluded that LES is a powerful tool in the simulation of ozone contactors. Zhang et al. (2013a, 2013b, 2014b) simulated the flow and tracer transport in the ozone contactor using the open-source numerical library OpenFoam and both the model and LES. Good agreement between the numerical data and the experimental data was obtained for cumulative residence time distributions. Demirel & Aral (2016) simulated mixing efficiency in multi chamber contact tanks based on vorticity field in combination with both and LES. Conversely, several researchers only used model to simulate residence time distribution in ozone contactors with different baffle configurations (Wols et al. 2008; Demirel & Aral 2018b; Goodarzi et al. 2020; Kizilaslan et al. 2020).

Although LES is able to better simulate the disinfectant mixing with the flow, LES requires substantially finer meshes than those used for two-equation turbulence models and a very long flow-time for performing statistics of the flow. Thus, an expensive computational effort is required in LES. Considering a compromise in the accuracy and computational effort, the present study simulates the flow in the ozone contactor using the Reynolds-averaged governing equations. The effect of two-equation turbulence models on the residence time distribution is investigated in detail.

The model constants ⁠, ⁠, ⁠, and take the values of 0.09, 1.44, 1.92, 1.0, 1.3, respectively.

The model constants ⁠, ⁠, and take the values of ⁠, 1.9, 1.0, 1.2, respectively, where ⁠.

A three-dimensional ozone contactor is shown in Figure 1. The ozone contactor has a cross-section of 230 mm240 mm and a length of 480 mm along the flow direction. Three baffles with the dimensions 180 mm230 mm evenly distribute along the vertical direction with an interval of 120 mm, dividing the ozone contactor into four chambers with the same dimension of 230 mm240 mm120 mm. The inlet has a dimension of 230 mm30 mm.

ANSYS Fluent is used to solve governing equations. The pressure–velocity coupling is treated using the SIMPLE algorithm. All convection terms are discretized with second-order upwind differencing scheme. When the residuals for all equations except tracer concentration are less than ⁠, the computations is assumed convergent. The residual criterion for tracer concentration is ⁠. Compared to the standard model, the computational efforts of RNG model, realizable model and SST model are 124, 140 and 160%, respectively. This is due to additional nonlinearities of these three models.

Residence time distributions computed from four turbulence models are shown in Figure 4. The experimental data from Kim et al. (2010a) are also included. All turbulence models capture three peaks with decreasing magnitudes on the curves of residence time distribution. The number of peaks was in accordance with that observed in the experiment. However, the magnitude of peaks for all turbulence models was greater than those experimental values, especially in the first peak. Accordingly, the computed residence time distribution is less than the experimental values after the normalized time is greater than 0.5. The initial peaks are 1.53, 2.01, 2.29, 2.54 for the standard model, the RNG model, the realizable model and the SST model, respectively, which is greater than the experimental value of 0.99. Among four turbulence models, the standard model obtains the lowest peak on the curve of residence time distribution. Correspondingly, the curve for the standard model is closer to the experimental curve than the other three turbulence models. Compared with the standard model, the first and second peaks of the other three turbulence models shifted to the left. The phenomenon demonstrates the existence of a short stream in the ozone contactor. However, the predicted values of the valley in the RTD curve by the RNG model, the realizable model and the SST model are very close to the experimental value.

The cumulative residence time distributions for four turbulence models are shown in Figure 5. The cumulative residence time distribution curves are obtained by integrating the residence time distribution curves. All turbulence models predict a relatively bigger values of cumulative residence time than the experimental values. This discrepancy is obvious in the initial period of the experiment. As time proceeds, all predicted curves tend close to the experimental values. In general, all turbulence models reproduce the cumulative residence time. Among the four turbulence models, the cumulative time distribution of the standard model is in better agreement with the experimental values. Therefore, the standard model has the best simulation effect on the internal water flow in the ozone contactor.

The experimental value is 111.25 s while the computed values are 109.87 s, 109.39 s, 108.52 s and 107.42 s for the standard model, the RNG model, the realizable model and the SST model, respectively. All computed values are in good agreement with the experimental value. It should be pointed out that the distributions of mean residence time at the outlet for different turbulence models are different.

The comparisons of dimensionless residence time for four turbulence models are shown in Table 1. All values of ⁠, ⁠, ⁠, and MDI for the standard model have the smallest error, showing the good capability in the simulation of the internal flow of the ozone contactor.

The velocity field at the mid-plane (⁠m) is shown in Figure 6. Multiple recirculation regions exist in the ozone contactor. In each compartment a big recirculation region and a small one are formed. Water moves mainly along a curved flow passage, as indicated by the green color in Figure 6. This curved passage determines the shape of residence time distribution at the outlet. All four turbulence models predicted the above feature. The difference lies in the maximum velocity in the curved flow passage. The standard model gives the maximum value of the maximum velocity, as shown in Figure 6(c). The patterns of the re circulation region in the first compartment are similar for four turbulence models. The standard and RNG models predicted the similar pattern of the recirculation region in other three compartments. However, the patters of the re circulation region in other three compartments are totally different for realizable and SST models. Especially, the flow velocity in the fourth compartment predicted by SST model is less than other three models. Thus, SST model gives the biggest magnitude of the first peak in residence time distribution. In general, velocity range predicted by the standard model was less than that by the other three turbulence models. That is, the tracer under the other three turbulence models can get to the outlet earlier, thus the first peaks in the RTD curve shifted to left.

The turbulent viscosity at the mid-plane (y = 0.115 m) is shown in Figure 7. The turbulent viscosity predicted by the standard and RNG models are similar in shape. However, the magnitude predicted by the standard models is the largest, so its hydraulic residence time is also the smallest. The patterns of the turbulent viscosity computed by realizable and SST models are different from those computed by the Standard and RNG models. In general, the magnitudes computed by RNG and realizable k- models and SST model are close.

Flow and tracer transport in the ozone contactor is conducted by using CFD. Residence time distribution is calculated based on the tracer concentration. All turbulence models capture the feature of residence time distribution and cumulative residence time distribution. The discrepancy between the experiment and all turbulence models is observed in the initial period. The standard k- model predicts the smallest peak and shifts the position of the peak to the right. The other three turbulence models obtained similar positions for the peaks, however a larger peak value was predicted value was predicted. All turbulence models reproduced the mean residence time at the outlet.

In terms of velocity and turbulent viscosity in the ozone contactor, multiple re-circulating region and dead zones exist in the reactor. Compared with the other three turbulence models, the standard k- model predicts the small velocity in the curved flow passage and a big value of turbulent viscosity. The difference in velocity field leads to the discrepancy in the residence time distribution.

All relevant data are included in the paper or its Supplementary Information.