Computational fluid dynamics (CFD) is a rapidly emerging field in wastewater treatment (WWT), with application to almost all unit processes. This paper provides an overview of CFD applied to a wide range of unit processes in water and WWT from hydraulic elements like flow splitting to physical, chemical and biological processes like suspended growth nutrient removal and anaerobic digestion. The paper's focus is on articulating the state of practice and research and development needs. The level of CFD's capability varies between different process units, with a high frequency of application in the areas of final sedimentation, activated sludge basin modelling and disinfection, and greater needs in primary sedimentation and anaerobic digestion. While approaches are comprehensive, generally capable of incorporating non-Newtonian fluids, multiphase systems and biokinetics, they are not broad, and further work should be done to address the diversity of process designs. Many units have not been addressed to date. Further needs are identified throughout, but common requirements include improved particle aggregation and breakup (flocculation), and improved coupling of biology and hydraulics.

INTRODUCTION

Computational fluid dynamics (CFD) has become an accepted method for process analysis of fluid flows in many industries. It recently has become widely used for analysis of hydraulic problems in water and wastewater treatment (WWT) but still needs to find wider acceptance for analysis of physical, chemical and biological processes in WWT. There are substantial financial and risk drivers to conduct CFD for better wastewater design (Wicklein et al. 2016). However, guidelines are limited and there are very few academic groups which focus on education or research into CFD in the wastewater sector. As such, a working group within the IWA Specialist Group Modelling and Integrated Assessment (MIA) was formed with the goal to encourage such a community to form. Laurent et al. (2014) described an alternative way of using CFD as a supplement to using simpler models. Wicklein et al. (2016) focuses on good modelling practice for CFD modelling of WWT. However, there also lacks an analysis of unit operations, including historic analysis of work focusing on the development of specific unit process approaches. The purpose of the current paper is to provide a review of the state of the art of applying CFD to analyze water and WWT plants, and to provide a critical assessment of future research needs.

The current paper is organized around plant unit processes where CFD has been used and which are particularly promising for future application. While many of the techniques apply to both clean water and WWT processes, the primary focus of the paper is on applications of CFD to analyze WWT and, specifically, to water resource recovery facilities (WRRF). The basic principles and function of unit operations are covered in well-known reference texts (Tchobanoglous et al. 2003). We limit our consideration to general methods solving for computational domains in either two or three dimensions (2D or 3D).

WHAT IS CFD

CFD provides a solution to the momentum and continuity equations for fluid mechanics. Numerical schemes for solution of these equations are necessary because these partial differential equations typically have no analytical solution, and hence the fluid domain is generally discretised in a grid or mesh scheme. Formulation of these equations in one dimension generally requires an assumption of homogeneity or symmetry in the other two dimensions, incompatible with geometry, such that CFD problems are almost always multidimensional (2D or 3D) or compartmentalized using a static approximation (Alvarado et al. 2012). CFD has been used for analysis of scientific problems and industrial processes since at least the 1940s. Presentation of the fundamentals of CFD theory is beyond the scope of this paper. For a detailed review of the techniques of CFD, refer to standard books on the subject, for example, Roache (1982), Patankar (1980), Fletcher (1991a, 1991b) and Ferziger & Peric (2002). A good introduction to the basic equations of CFD for application to activated sludge processes is included in Karpinska & Bridgeman (2016).

APPLICATION OF CFD TO WATER AND WWT

We discuss the application of CFD to processes and problem areas specific to WWT. We proceed through the normal flow stream in a WRRF, but begin with hydraulic elements that are found in almost all WWT facilities, flow splitting and other hydraulic transport facilities.

Flow splitting and evaluation of head losses

Flow splitting is a critical unit operation that enables balanced flow to multiple units across a range of flows. They are generally based on flow over a static weir, and hence hydraulics are fundamental to their function. CFD has been used relatively extensively in engineering practice for analysis of flow splitting between process units and for estimation of complex head losses in hydraulic profiles. Not a great deal of this practical work has been reported in the literature, however. Figure 1 presents a visualization of a 3D CFD flow splitter simulation developed at a recent workshop sponsored by the CFD working group, Marques (2015a).
Figure 1

Surface velocity profile for a flow splitter from open source CFD software (Source:Marques 2015a).

Figure 1

Surface velocity profile for a flow splitter from open source CFD software (Source:Marques 2015a).

Hassan et al. (2014) present results from CFD analysis on a tapered longitudinal manifold and a uniform longitudinal manifold. Two manifold configurations were tested at different inlet flows, and results suggested that the tapered manifold provided relatively equal flow distribution compared with the uniform longitudinal manifold. Knatz (2005) indicated that the influent direction relative to the channel may impact the results.

Tong et al. (2009) used CFD to investigate balancing the flow through a wide range of manifold geometries. Results showed that optimal flow uniformity could be achieved by expansion of the cross-sectional area, linear or non-linear tapering of the distribution manifold or varying the cross-sectional area of the outflow channels modifications.

Research needs

Research work has focused on general flow distribution, as fluid flow manifolds are ubiquitous in engineering practice, from fuel cells to chemical reactors. However, there is very little peer-reviewed research that is specific to flow splitting in water and WWT processes. A key limitation that has not been addressed in the literature is the potential impact of solid and gas phases. Solids may impact splitters by differential movement of particulates within the splitter, which may increase viscosity or density and hence induce differential flow (see the relevant section in this paper). The gas phase, particularly in aeration, can have a strong impact on fluid density and momentum (where momentum is imparted from an aerator, for example). This is critically important where a splitter has a particularly turbulent inlet cell, or where splitters are used to distribute flows from an aerobic unit to multiple clarifiers, particularly where centrifugal or laterally directed aeration is used.

Grit removal

Grit chambers use gravity or centrifugal sedimentation to separate large, dense particles from raw wastewater. While the principles are relatively simple, the multiphase nature, and multiple mechanisms can make analysis complex. Analytical evaluation of grit removal goes back to the work of Camp (1942) who developed a rational approach for sizing of grit removal channels based on ideal settling behaviour. Much of current practice, however, relies on manufacturer's recommendations without an analytical basis. CFD provides an alternative to reliance on manufacturer's claims, particularly where the hydraulic configuration mixes gravity and centrifugal sedimentation, such as in a vortex separator.

McNamara et al. (2012) present a comprehensive evaluation of three different types of grit removal tank geometries: forced vortex, detritor and lamella. Grit particles of nine different diameters were converted to a continuous distribution equation and modelled with specific gravities of 2.65 based on silica sand and 1.5 based on laboratory samples from field installations and a sphericity ratio of 0.65. Multiphase (water and air) simulations were carried out to steady state prior to injection of grit particles into the inlet stream.

Research needs

Recent work on grit removal has included many desirable elements of good CFD analysis: efforts at calibration or verification, a 3D approach and multi-phase analysis. The best work appears to have included analysis of solids transport and discrete settling. It is not so clear that underflow concentrations have been monitored, however. It has generally been assumed that grit settlement is not density-coupled. A particular opportunity is the use of approaches from other unit operations such as population balances (Nopens et al. 2002; Nopens 2005) to describe performance under dynamic conditions. While sedimentation in the primary unit is generally unhindered, there may also be links to other sedimentation approaches in primary and secondary units, that particularly hindered settling in solids collection zones.

Primary sedimentation

Primary sedimentation exhibits flocculation, discrete, hindered, and compression settling of near neutral buoyancy colloidal mineral and organic particulates. Process performance is highly influenced by flow, including those influenced by multiphase solid–liquid interactions in sludge blankets. These factors make it a clear target for the application of CFD. As such, primary sedimentation was one of the first unit processes to receive attention from CFD researchers.

A number of analytical approximations have been taken to simplify multidimensional clarifier geometries into a single dimensional finite difference problem, mainly by imposing radial homogeneity or symmetry. Takamatsu et al. (1974) applied radial symmetry and a floor boundary condition, together with discretization in the vertical dimension to identify the optimal depth of a clarifier. The boundary condition for the bottom (sludge) boundary identified in this work has been widely used.

One of the first multi-dimensional numerical models of primary sedimentation was introduced by Imam et al. (1983). The model used a finite difference discretization of the governing equations to simulate the settling of several classes of solids in the flow domain. Results were compared to several different theoretical estimates by Camp (1946) and showed a more realistic lower rate of removal. The work assumed neutral density and, therefore, would not be expected to be effective in adequately predicting the influence of underflow or sludge blanket solids concentrations.

Abdel-Gawad & McCorquodale (1984) presented a strip integral numerical model to simulate the performance of primary clarifiers, with emphasis on the prediction of the velocity field and concentration distribution. The hydrodynamic sub-model was calibrated using a measured velocity distribution in a physical model. Solids were modelled as classes of discrete particles with settling velocities based on batch test. The model was calibrated by measurements in full-scale rectangular tanks. The predicted concentration profiles and removal efficiency were in good agreement with the measured values. The sludge blanket and underflow, however, were not modelled.

A 2D, neutral density, turbulent CFD model of rectangular primary sedimentation tanks was developed by Stamou et al. (1989) who compared predicted solids profile and residence time distribution (RTD) curves to field measurements. Turbulent flow was modelled using a k-ɛ approach of Rodi (2000). They found that variation in the turbulent Schmidt number from 0.5 to 1.0 resulted in little difference in the flow through curve. Wang & Maxey (1993) explore the problem of discrete settling in a flow field of homogenous turbulence from the perspective of theoretical fluid mechanics. This is sophisticated work with considerable attention to numerical and experimental issues. They produce results for the increase in mean Stokes drag settling speed in uniform turbulence of zero mean velocity (batch conditions).

A generalized settling model (GSM) that includes a model for hindered settling in addition to discrete settling was presented in Mazzolani et al. (1998). This was specifically intended to improve upon discrete settling models and ‘monodisperse settling models’ that do not recognize that typical sedimentation tanks for water and wastewater ‘typically treat highly heterodisperse suspensions.’ They discuss the difference of their model from the single exponential Vesilind (1968) and double exponential model of Takacs et al. (1991). They positively compare results of a 2D numerical simulation of their GSM to discrete and basic hindered models.

Griborio et al. (2014) provide a report on a comprehensive evaluation of two primary sedimentation tanks evaluated with 2D and 3D CFD models. The projects included field testing and evaluation of alternative geometries and recommendations on improvement. Notably, the work with the 2D model included full solids transport with density couple, a five-component settling model including a compression model and flocculation using the 2Dc/3Dc model (Griborio 2004). The 3D model did not include these features, but was used to estimate velocity profiles in the inlet and outlet.

Research needs

Primary sedimentation was one of the first areas of water treatment to be addressed using CFD methods. Much of the early work was done in 2D and in relatively coarse grids in custom programs, with a key focus on neutral density hydraulics rather than sedimentation performance. Typically, underflows have been ignored, in spite of the fact that sludge thickening is an important part of the operation of primary sedimentation tanks for WWT. Future work should include analysis of the sludge blanket using appropriate sedimentation models which include hindered and/or compressive settling. There is a need for development of sedimentation models that may include multiple particle distributions for input to the CFD models which would allow for a more accurate representation of effluent quality. Almost all work to date has assumed neutral density conditions. This is certainly not appropriate for sludge blankets, where the presence of solids contributes to fluid density. So density couple should be included in future work including these regions, either by a drift flux model or by an active scalar approach. There is a need for future work using high-resolution 3D models calibrated to field solids profile and settling tests. Only the work of Griborio et al. (2014), considered here, includes effects of flocculation and this is likely a key issue. Emerging alternatives to primary sedimentation such as rotating belt filters may also benefit from application of CFD, as they involve multiple mechanisms, including sedimentation, mechanical-hydraulic coupling, and multiphase interactions (Paulsrud et al. 2014).

Biological processes (suspended growth)

The focus on suspended growth (flocculent) systems has been in activated sludge basins. Anaerobic digesters are a separate problem addressed below. Activated sludge tanks have a broad range of functionality, including nutrient and carbon removal, pathogen destruction, and removal of micro pollutants. They are also generally compartmentalized, have large recycle streams, and are critically dependent on multiphase contact and effective hydraulics. There are therefore strong potential benefits offered by CFD, including assessing hydraulic behaviour, gas–liquid transfer and biological functionality. At the same time, there are major challenges, including turbulent hydraulics, a multiphase nature (including potentially non-Newtonian fluid behaviour), and biokinetics.

A very comprehensive review is provided by Karpinska & Bridgeman (2016) for CFD of activated sludge reactors. This includes a critical review of (1) Reynolds averaged Navier-Stokes (RANS) simulations, (2) turbulence models, and (3) multiphase modelling, with a strong focus and discussion of the need to move to coupled CFD-biokinetic modelling. They conclude, ‘The complete CFD simulation of the complex multiphase flow in AS tanks remains a challenge, due to the high CPU and RAM requirements and limited feasibility resulting from the imposed convergence criteria. Although there is still no unequivocal protocol on CFD methodology, the most computationally efficient scenario, RANS/unsteady RANS (URANS) closed by a k-ɛ turbulence model has been adopted as the standard for the modelling of AS tanks …’

Within the area of mixing modelling, efforts have been made in activated sludge tanks by estimation of velocity and solids profiles. Samstag et al. (2012) showed that if density couple was not included, mechanical mixing in an activated sludge reactor was significantly overestimated. They used a 3D commercial CFD model with multiphase simulation of water and air and an active scalar transport model for solids calibrated to field tests. Le Moullec et al. (2008) used a multiphase 2D Euler-Euler scheme and simulation of particle tracking in a Lagrangian reference frame using a commercial CFD package to model velocity profiles and RTD in an aerated channel whose characteristics had been previously measured at laboratory scale (Potier et al. 2005). Tracer experiments were simulated using a passive scalar approach. Influence of solids gradients on fluid flow was not modelled.

Flocculation in activated sludge influences a number of factors, including solid phase characteristics, and potential biological activity. Parker et al. (1971, 1972) evaluated factors influencing flocculation in activated sludge mixed liquors. The work did not include CFD, but they proposed a simple model for floc breakup and agglomeration which has been used by subsequent researchers in full CFD models of sedimentation. The model (Parker et al. 1972) proposed that floc breakup and agglomeration could be related to the root mean velocity gradient, G. In contrast to this, Ducoste & Clark (1998) found in experiments that important parameters were controlled by the turbulence intensity and not by G. Nopens et al. (2002) and Nopens (2005) present results from experimental testing and calibration of a population balance model for flocculation in activated sludge. While a promising alternative approach to the Parker et al. (1970, 1971) models, the authors conclude that model improvement is needed.

There has been extensive work over the last 10 years on coupled biokinetic-hydraulic models (since computing capabilities made this possible), generally coupling CFD with variants of the IWA ASM series models (Henze et al. 2000). This can be divided into statically linked models where CFD is solved and biokinetics overlain or dynamically linked models where both are linked and the biokinetics solved together.

Laursen (2006) completed a very comprehensive study of the hydrodynamic and biokinetic modelling of activated sludge applied to full-scale WWTP case studies. Commercial software was used to develop full 3D CFD simulations of three different full-scale aeration tank geometries. Features included: (1) biokinetic modelling using the ASM3 model (Henze et al. 2000), (2) active density coupling of solids concentrations, (3) liquid turbulence simulated by k-ɛ and shear strain transport models with air bubbles and sludge flocs modelled using a zero equation model, (4) air diffusers modelled as bubbly flow calibrated to detailed laboratory velocity and air fraction measurements, (5) propeller mixer modelled by both sliding mesh and momentum source models, and (6) calibrated viscosity models. Interesting practical problems were considered in three case studies.

Littleton et al. (2007) used a 3D commercial CFD model to simulate fluid flow in a closed loop reactor with aeration and consumption of dissolved oxygen (DO) simulated using a supplemental equation with a goal of identifying zones where simultaneous nitrification–denitrification was likely. The CFD model was validated with field data obtained from a test tank and a full-scale tank. Solids gradient influences on the flow pattern were not simulated.

Le Moullec et al. (2010a) compared pilot plant results to three different integrated models including simulation of hydrodynamics and biological reactions using the ASM1 model (Henze et al. 2000): (1) continuously stirred tank reactor (CSTR) and axial dispersion models, (2) a full 2D multiphase Euler-Euler CFD model integrated with ASM1 kinetics, and (3) a compartmental model in which coarse grid velocity components were determined by CFD independently of the biological kinetics and then the kinetics applied to the steady state velocity field determined by the CFD model. The compartmental model well predicted measured DO concentrations in the range of 2 to 4 mg/L, better than either the systemic model or the full CFD model. All three models over-predicted measured chemical oxygen demand (COD) concentrations. The two CFD models did a better job predicting nitrate concentrations (in the range of 30 to 60 mg/L) than the systemic model. All three models under-predicted ammonia concentrations. None of these models incorporated the influence of solids concentration gradients on the velocity profile. Additional results from the full multiphase (air and water) CFD model are reported in Le Moullec et al. (2010b).

Sobremisana et al. (2011) simulated hydrodynamics, floc dynamics, and biological reaction kinetics for activated sludge. A planar 2D CFD hydrodynamic model was developed for a baffled flow-through reactor using a commercial CFD package. Constant density was assumed. The quadrature method of moments was used to estimate floc aggregation and breakup. This solution was integrated with the hydrodynamics through user-defined subroutines. The ASM1 model was implemented using a convection and diffusion application of the commercial software with rate expressions for species reaction defined by ASM1. Results were not compared to field or pilot-scale results or to the results from CSTR models.

A 3D single phase CFD simulation of an oxidation ditch configuration was implemented by Pereira et al. (2011) to determine RTD characteristics. Three different turbulence models were compared: RANS with the standard k-ɛ model; URANS; and Large Eddy Simulation. Once this was accomplished, CSTR and plug flow reactor models incorporating an ASM1 biokinetic models were fitted to the RTD characteristics identified in the CFD simulation.

Rehman et al. (2014) presented the results of application of an integrated hydrodynamic and biokinetic model to the distribution of velocity, DO and ammonium in a full-scale closed loop reactor. Tank hydrodynamics were modelled in 3D using an Eulerian two-fluid model for liquid and gas phases with a commercial CFD package. A realizable k-ɛ model was used to model the effects of turbulence and a drift flux model for dispersion of bubbles. The tank was modelled with a free water surface. Mixing propellers were modelled as momentum sources. Biokinetics were modelled using the ASM1 model with addition of an oxygen mass balance to model transfer of oxygen to the liquid phase. Bulk density was calculated based on local suspended solids concentration. Results were compared to field sampling from a full-scale reactor and 15% improvement in results was observed. Results (presented in Figure 2) show significant variation in DO and ammonium concentrations, justifying the greater (1–2 day) simulation time compared to a CSTR model. Impact of different mixing conditions on the system performance was observed.
Figure 2

Oxygen (a) and ammonium (b) concentration plots in a closed-loop reactor (Source:Rehman et al. 2014).

Figure 2

Oxygen (a) and ammonium (b) concentration plots in a closed-loop reactor (Source:Rehman et al. 2014).

Laurent et al. (2014) present a comparison of the merits of the integrated CFD and biokinetic modelling compared to compartmental models using CFD to establish generalized velocities prior to subsequent biokinetic modelling. Example data from Alvarado et al. (2012) and Le Moullec et al. (2010a) are discussed. Ratkovich et al. (2013) provide a critical review of activated sludge rheology models.

A critical review of the literature relating to hydrodynamic and biokinetic modelling of membrane bioreactors (MBRs) was provided by Naessens et al. (2012), with many issues common to activated sludge, but with the additional consideration of membrane-fluid interaction (including fouling management). Experimental and CFD work providing the background to this work is presented in Ratkovich (2010). Saalbach & Hunze (2008) provide a specific example in a multi-compartment system. Apart from hydraulics, CFD has been shown to be an effective tool in membrane fouling prediction, mainly through estimation of membrane shear rate (Boyle-Gotla et al. 2014). The latter example also demonstrates application to anaerobic MBR systems.

Research needs

The work reviewed reveal that activated sludge tank modelling is a well-developed field that showcases application of CFD to wastewater problems. CFD has been generally used to gain insight into the process, not possible through other techniques that have identified significant deviations from mixed or CSTR approaches. Highlights include incorporation of biokinetic, solids and air transport, and rheological models into CFD models for suspended growth biological treatment systems. The most comprehensive work has included: (1) 3D CFD, (2) sedimentation and solids transport with active density couple, (3) ASM3 biokinetics, (4) calibrated impeller mixing modelling, (5) aeration, and (6) modelling of non-Newtonian viscosity effects. There are still possible extensions to coupling flocculation and CFD, and consideration of interactions at the micro-scale has been limited, but likely the key need is broader application of these techniques, given the diversity of activated sludge process designs, and demonstrated value of CFD done to date. There is also an emerging need to apply CFD techniques to emerging low energy units, such as granular activated sludge, anaerobic mainline treatment units (including anaerobic MBR), suspended carrier systems, and mainline and side stream anaerobic ammonium removal (which is critically dependent on local conditions).

Secondary sedimentation

Secondary sedimentation would appear to have similar challenges to primary sedimentation, but is actually governed by some different mechanisms, including near neutral solids density, prominent hindered and compressive settling behaviour and higher underflow rates. Modelling goals are also directed by the multiple functions of final effluent clarification, activated sludge thickening, sludge storage and flocculation. Secondary sedimentation was one of the first unit processes to receive attention from CFD researchers. Summary descriptions of some of the most important research follow. This section may be considered as an update to Ekama et al. (1997), which contains a comprehensive summary of earlier work in analysis of secondary settling tanks.

McCorquodale and his students and associates at the University of Windsor and the University of New Orleans have been leaders in application of CFD to sedimentation, using customized computer codes based either on the vorticity/stream function method of Roache (1982) or the methods of Patankar (1980). Zhou & McCorquodale (1992a) investigated 2D flow in a radial flow (circular) clarifier. They performed simulations using their Patankar (1980) CFD code incorporating turbulent flow (k-ɛ turbulence model), solids transport, and settling by a double exponential function (Takacs et al. 1991). The model also included coupling of the concentration profile with the fluid flow through fluid density. They compared the resulting velocity profile in their model for the cases with and without solids input and underflow pumping. Their results demonstrated the ‘density waterfall’ that occurs in radial flow clarifiers as a result of solids settling immediately after introduction at the tank inlet. Their comparisons in CFD and physical model tests showed that with no solids present, the velocity pattern in the tank is completely different from when solids are included. They investigated sedimentation in a tank with three different feed well diameters. Results showed that performance was best for the tank with the smallest feed well. Results from the larger feed well were very similar to results from simulations of the case with no feed well at all. More general applications of this CFD technique were presented by these authors for rectangular clarifiers in Zhou & McCorquodale (1992b) and for circular clarifiers in Zhou & McCorquodale (1992c). Other research by McCorquodale and his associates has been crucial to development of the state of the art of clarifier modelling, including McCorquodale et al. (1991) and McCorquodale & Zhou (1993). Griborio (2004) covers development and validation of a five-component settling model, flocculation models, and details for quasi 3D CFD for activated sludge clarifiers. This CFD model uses a vorticity/stream function approach to eliminate pressure from the fluid equations and a simple mixing length turbulence model. This work also contains an extensive reference list.

Flocculation (see activated sludge section) is also linked to clarifier performance. The impact of flocculation processes on secondary clarifier performance via simulation was extensively assessed within McCorquodale's group and is detailed in Griborio (2004). Griborio & McCorquodale (2006) used this model to investigate the influence of center-well geometry on flocculation and clarifier performance. They found that the major benefit of optimum center-well geometry is in improving hydrodynamic performance and that flocculation had less influence. The same model was used by Gong et al. (2009) in analysis of sedimentation in a rectangular sedimentation tank using a 3D turbulent commercial CFD model.

Armbruster et al. (2001) present results from use of the mathematical model presented in Lakehal et al. (1999). Results were compared to experiments by Krebs et al. (1998). Concentration profiles from simulation of dynamic loading over 24 h of flow based on data from a treatment plant in Germany were presented. De Clercq (2003) developed a 2D CFD model in a commercial package incorporating solids transport, density couple, and flocculation. The model was applied to a radial flow (circular) activated sludge clarifier. A Herschel Bulkley rheological model was incorporated by user-defined functions.

A 2D finite element analysis of flows in secondary settling tanks was presented in Kleine & Reddy (2005). They incorporated solids settling using a double exponential function (Takacs et al. 1991) and included the influence of density on the momentum equations. The k-ɛ equation was used to simulate turbulence and compared to a constant turbulent viscosity approach. The model was compared to field tests for radial flow circular activated sludge settling tanks and to results from the commercial sedimentation program, SettlerCAD. In comparison to field results the best fit of CFD results was with a Schmidt number greater than 1.

Burt (2010) developed 2D CFD models calibrated by field and laboratory tests. The CFD models were constructed in the commercial software using an algebraic slip model with user-defined functions for definition of density, settling velocity and rheology. An extended drift flux model was compared to a multiple drift flux model which tracked 10 different size groups. A solids profile developed in a recent CFD workshop by the drift flux method of Brennan (2001) is shown in Figure 3.
Figure 3

Solids profile for a secondary sedimentation CFD simulation developed in open source software (Source:Marques 2015b).

Figure 3

Solids profile for a secondary sedimentation CFD simulation developed in open source software (Source:Marques 2015b).

Research needs

Activated sludge secondary sedimentation tank simulation is the most well-developed area of application for CFD in WWT. Initial models were only 2D, but almost all included solids transport and settling with coupling of the solids concentration field to tank fluid flow. A significant improvement has been made with incorporation of GSM including discrete, hindered, and compressive settling regimes and flocculation. The work of Ducoste & Clark (1998) suggests that the relatively widely used Parker et al. (1970, 1971) model (for activated sludge flocculation) may not be adequate to capture the influence of flocculation on behaviour of sedimentation tanks, and flocculation and particle interaction has not been included in detail (but is empirically included through scalar compression settling models). Future work should incorporate higher resolution 3D geometric models including GSM and models for flocculation, preferably verified by field tests for solids profile and sludge settling velocity. Hindered settling is typically represented by empirical equations such as the Vesilind or Takacs exponential equations; future work should attempt to further validate physically-based compression models such those of Kinnear (2002) and Bürger et al. (2011). Additionally, models should incorporate the entire settling domain from the inlet pipe to the effluent and underflow outlets. Knowledge gained from CFD should also be used to improve 1D models for plant-wide simulation as developed in Guyonvarch et al. (2015).

Solids handling

Dissolved air flotation

Dissolved air flotation (DAF) is used in water and WWT for solids separation in lieu of gravity sedimentation and for sludge thickening. Amato & Wicks (2009) presented the results of a CFD study of DAF for separation of solids from a pre-coagulated surface water supply. A multiphase Euler-Euler model was used to simulate liquid and air hydrodynamics. A k-ɛ turbulence model was used in commercial CFD software (ANSYS Fluent v.6.3.26). The volume weighted average vorticity was extracted from the CFD model as a measure of floc-bubble agglomeration disturbance, with an average floc-bubble agglomerate diameter of 148 μm in the clarification zone. Floc characteristics were inferred from bubble concentration. These assumptions were used to calculate the location of the ‘white water level’ which previous work had correlated with good solids removal (see Figure 4).
Figure 4

CFD Predicted white water level and velocity vector plots in a DAF tank, (left) without and (right) with subnatant tubes (Source:Amato & Wicks 2009).

Figure 4

CFD Predicted white water level and velocity vector plots in a DAF tank, (left) without and (right) with subnatant tubes (Source:Amato & Wicks 2009).

Anaerobic processes

Anaerobic digesters in a wastewater context are relatively high solids (in-reactor 1–3%), with performance highly dependent on hydraulics. Operating cost of the digester, as well as its overall functionality, is critically linked to digester mixing (Verhoff et al. 1974). Given that capital costs of digester can be very high (due to large volumes), it is critical that the geometry and mixing systems are appropriately designed. Key issues around poor mixing include short circuiting (critical), dead volume (should be minimized), and plug-flow behaviour (important to note, but not critical to performance). There has been limited work on anaerobic digester systems compared with activated sludge and clarifiers and hydraulics and CFD has been noted as a key research need in anaerobic digestion modelling as a whole in a recent review (Batstone et al. 2015).

A critical issue in CFD of digesters is non-Newtonian behaviour of the solids, which is generally shear thinning, and is influenced by temperature and solids concentration. This behaviour is generally modelled by Bingham or Hershel Bulkley models (or a combination of the two) and sludge rheology in detail is reviewed in Eshtiaghi et al. (2013). Sludge rheology can cause digesters to exhibit unexpected and dynamic behaviour (see needs below), due to formation of unmixed ‘thick’ zones.

The majority of commercial and academic work has been non-reactive hydraulic analysis. Wu & Chen (2008) discuss a general mathematical model that predicts the flow fields in a mined-flow anaerobic digester. In this model, liquid manure was assumed to be a non-Newtonian fluid and the flow governed by the continuity, momentum, and k-ɛ turbulence equations and a non-Newtonian power law model. Commercial CFD software was applied to simulate the flow fields of laboratory-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonian fluids flow in a laboratory-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solids (TS) concentration in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results. This was extended in Wu (2009a) with application of a 3D commercial CFD model to anaerobic digestion. The model incorporated the k-ɛ turbulence model, and predictions of pseudo-plastic fluid behaviour based on equations for viscosity and density. The density calculation included the influence of solids concentration, but solids transport and settling was not included, so density effects of solids concentrations gradients were ignored. The model included a multiple reference frame (MRF) approach to model impeller rotation within a MRF zone inside a stationary reference frame. The model was applied to the simulation of mixing with four different mixing systems: mechanical mixing through propellers in external draft tubes, mechanical stirring by side-entry propellers, mechanical pumping by a propeller in an internal draft tube and mechanical stirring by a top-entry propeller. Wu (2009b) presents a CFD simulation of an egg-shaped digester with mechanical draft tube mixing. CFD techniques were similar to those of Wu (2009a).

Wu (2010) presents an Eulerian multiphase flow model that characterizes gas mixing in anaerobic digesters. Liquid manure was assumed to be a non-Newtonian pseudo-plastic fluid that is dependent on TS concentration. Twelve turbulence models were evaluated by comparing the frictional pressure drops of gas and non-Newtonian fluid two-phase flow in a horizontal pipe obtained from CFD with those from a correlation analysis. Commercial CFD software was used for the work. The simulation results in a small-sized digester were validated against experimental data from literature. Comparison of two gas mixing designs in a medium-sized digester indicated that mixing intensity is insensitive to the TS in confined gas mixing, whereas there are significant decreases with increases of TS in unconfined gas mixing. Moreover, comparison of three mixing methods indicated that gas mixing is more efficient than mixing by pumped circulation, while it is less efficient than mechanical mixing. This work did not, however, include solids transport and sedimentation, nor did it include simulation of the effects of solids concentration gradients on density and fluid flow.

Results of development of a CFD model to simulate mechanical mixing of sewage sludge at laboratory scale were presented in Bridgeman (2012). The work used the commercial meshing and CFD software. Five different turbulence models were compared. Meshes with 280,000 to 1,600,000 cells were used. An MRF model was used to generate velocity fields around rotating impellers. Velocity profiles in tanks with different solids concentrations were developed, but solids transport and settling was not modelled, so that the influence of solids concentration gradients on the flow was not simulated.

Gaden (2013) presents work resulting in development of a CFD model for anaerobic digestion implemented in the open source CFD platform, OpenFOAM. The model implements a version of the Anaerobic Digestion Model No. 1 (ADM1) in a 10 × 10 2D square grid. The model is two-phase (gas and liquid). Buoyancy effects from temperature gradients are included but density impacts from solids concentration gradients are not.

Research needs

Digestion studies to date have treated high solids concentrations as affecting bulk density, but spatial distribution of solids and the impact of density gradients on fluid flow patterns have not been explored. This is critical to enhanced use of CFD in digester simulations, and may enable exploration of mechanisms such as foaming (Dalmau et al. 2010), which is a critical operability issue. In addition, foaming can even lead to digester-wide issues such as fluid inversion. Incorporation of biokinetic models into density coupled 3D CFD models will become increasingly important for modelling of digesters to properly consider these effects, as well as the impact of incomplete mixing on the biology, which may include formation of zones with specific activity. There is also a strong need to consider emerging processes such as plug-flow, and leach bed systems (Batstone et al. 2015), and the impact on ancillary processes such as heat exchangers.

Disinfection

Ultraviolet

CFD modelling of ultraviolet (UV) reactors is fast becoming a standard approach for characterizing, designing, and troubleshooting the UV disinfection performance. Moreover, growing confidence in numerical models that have been validated with extensive biodosimetry data have led UV manufacturers to use the tool as part of an on-line algorithm for dose monitoring. Numerical UV disinfection models are complex and require the proper execution of several components so that the numerical results can be used for analysis of a UV process. UV disinfection models can be divided into three major components. These major components include: (a) fluid flow/turbulence model, (b) fluence rate distribution model, and (c) microbial transport model. As the name implies, the fluid flow/turbulence model involves characterizing the spatial variations in fluid flow and turbulent mixing that occurs in the UV reactor. The fluence rate model involves characterizing the spatial variations in the UV light intensity in the UV reactor. Finally, the microbial transport model involves characterizing the movement of the microorganisms through the UV reactor.

A number of research studies have been performed to assess CFD UV process performance as a function of the fluence rate model selection (Liu et al. 2004; Ducoste et al. 2005a, 2005b; Wols 2010), turbulence model selection (Liu et al. 2007; Wols 2010) and the approach used to simulate the transport of microorganisms (i.e. Eulerian or Lagrangian approaches) (Ducoste et al. 2005a, 2005b; Sozzi & Taghipour 2006). In drinking water treatment applications, a significant effort was made to demonstrate the accuracy of these models for several reactor designs and different microbial disinfection kinetics (Ducoste et al. 2005a, 2005b; Wols et al. 2010). In addition, the UV dose distribution, which was exclusively an output from the CFD model by simulating the transport of particles (i.e. Lagrangian approach) within the reactor and monitoring their exposure to local UV light intensity along the particle path, was only validated indirectly through the model's ability to predict the experimental effluent log inactivation. Researchers were able to develop an experimental Lagrangian approach that involved tracking fluorescent polystyrene microspheres through a UV reactor and monitoring the change in fluorescence due to its cumulative exposure to UV light (Bohrerova et al. 2005; Blatchley et al. 2006; Zhao et al. 2009). While this approach has its limitations, it has provided additional information about the accuracy of CFD UV disinfection models and, in combination with experimental log inactivation, improves the validation process of UV reactors.

A particular concern in WWT is the disinfection of water containing particle aggregates. Researchers have shown that bioflocs that shield or harbour microorganisms can reduce the UV disinfection performance (Mamane & Linden 2006; Caron et al. 2007; Kollu & Ormeci 2012). Experimental results suggest that floc size, number of microbes incorporated into the floc, and the spatial location of these organisms within the floc can influence the UV dose to achieve a high log inactivation (Mamane & Linden 2006). Mamane et al. (2006) explored the effect of light scattering on measurement of UV absorbance and penetration of germicidal UVC irradiance in a UV reactor. As part of that study, CFD was used to evaluate the radiative transfer equation in predicting the UV fluence rate within a reactor. Mamane et al. (2006) results showed that the model over-predicted the fluence rate in wastewater effluent augmented with particles. The researchers hypothesized that the higher model results was due to the type and size of particles in the augmented wastewater solution, which was augmented with irregular, 2–5 micron particles that scattered light anisotropically. The anisotropic nature of the scattered light was not modelled in their study.

Disinfection

Chemical oxidation

Greene (2002) researched the fate of chlorine and bacterial pollutants in chlorine contact tanks treating wastewater effluent. An Euler-Euler approach was used for simulation of microbial inactivation with the spatial distribution of microorganisms in the reactor viewed as a continuous field, similar to a dissolved species. Disinfection models were implemented in the general purpose commercial CFD software. Reactor tanks were modelled in 3D using a k-ɛ turbulence model. Buoyant forces were assumed to be negligible. Grid independence checks were undertaken with a mesh of 132,000 cells selected for the influent piping and 790,000 cells for the reactor. Santoro et al. (2015) used CFD as a deterministic tool to identify probabilistic curves for pathogen deactivation by peracetic acid, identifying the value of CFD for protyping of systems where there are complex mechanisms present, and enabling simple tools for end-user application.

Research needs

Application of CFD to disinfection is relatively well developed. It is normally assumed that disinfection flows are not affected by solids density or other buoyant forces. Hence neutral density simulations are typical and this has seemed to be a reasonable assumption. To date, no CFD model has been developed to explore the performance of UV disinfection in wastewater containing particle aggregates. The ability to model such a system may require the simulation of continued aggregation within a UV reactor, the floc size distribution, and UV light path length, absorbance, and potential scattering due to the presence of these aggregates.

CONCLUSIONS

Analysis of the general use of CFD in WWT has identified that the sophistication of the technique is highly variable between different units. In particular, CFD simulation of secondary sedimentation is highly mature, while work in anaerobic digestion is less well developed. Nowhere (except possibly disinfection) is CFD used in a widespread or routine way as a design, risk-management, or troubleshooting tool. This offers clear opportunities to further develop the value of CFD in wastewater process evaluation.

  1. While projects which assess the general flow distribution between units are widespread in engineering practice, there is a need for more peer-reviewed research specific to flow splitting and head loss determination in water and WWT processes. The potential impacts of solid and gas phases on flow distribution should be addressed in future models.

  2. The common assumption that grit settlement is not affected by density gradients should be demonstrated by comparative studies.

  3. There is little work on the analysis of sludge blankets for primary sedimentation. CFD models in 3D, incorporating the entire tank domain and including discrete and compressive settling and improved flocculation and rheology models, should be considered in future work.

  4. Alternative models for flocculation should be compared to the dominant empirical model and these included more routinely in CFD analysis of activated sludge basins and final sedimentation.

  5. CFD coupled to activated sludge biochemical models has been demonstrated to be very valuable compared with simpler mixed tank models. This should be further expanded to include models such as the ASM2d and ASM3 models incorporating phosphorus removal. Incorporation of density-coupled solids transport should be included in future suspended growth reactor CFD models since solids settling affects the solids concentration, density and velocity profiles and resulting reactant concentrations. There is also a continuing need to use CFD models for validation of biokinetic models based on simpler hydraulic assumptions.

  6. More sedimentation tank modelling should be done in 3D, incorporating full GSM and models for flocculation and rheology. Alternative physically-based models for compression settling should be compared to the dominant empirical models.

  7. Future work in modelling of digestion should include the effects of density couple, hindered settling, compression and rheology. Incorporation of biokinetic models into anaerobic digestion study is in its infancy and could be critical to advanced issues such as foaming and inactive zones.

  8. Disinfection modelling using CFD is relatively well developed but modelling of floc aggregates should be explored in future work.

  9. There are potential applications for CFD outside of the areas considered here, such as final dewatering, particularly through screens, which may avoid primary unit elevation and reduce catchment pumping costs and centrifuges (enabling reduced energy and polymer consumption and unit wear), other solids handling units such as screws and conveyor belts, centrifugal and positive displacement transport of liquids and gases and behaviour of fluids and particulates during transport (mainly in pipes).

  10. Whole plant hydraulic modelling is also a major opportunity for the optimization of design and operating costs, although this is obviously a significant computational challenge.

ACKNOWLEDGEMENTS

This work has been accomplished through a cooperative effort by members of the International Water Association working group on CFD. Volunteer efforts by all members are appreciated by the authors.

REFERENCES

REFERENCES
Abdel-Gawad
S. M.
McCorquodale
J. A.
1984
Strip integral method applied to settling tanks
.
Journal of Hydraulic Engineering
110
(
1
),
1
17
.
Alvarado
A.
Venantam
S.
Goethals
P.
Nopens
I.
2012
A compartmental model to describe hydraulics in a full-scale waste stabilization pond
.
Water Research
46
(
2
),
521
530
.
Armbruster
M.
Krebs
P.
Rodi
W.
2001
Numerical modelling of dynamic sludge blanket behavior in secondary clarifiers
.
Water Science and Technology
43
(
11
),
173
180
.
Batstone
D. J.
Puyol
D.
Flores-Alsina
X.
Rodríguez
J.
2015
Mathematical modelling of anaerobic digestion processes: applications and future needs
.
Reviews in Environmental Science and Biotechnology
14
(
4
),
595
613
.
Blatchley,
E. R.
III
Shen
C.
Naunovic
Z.
Lin
L.
Lyn
D. A.
Robinson
J. P.
Ragheb
K.
Grégori
G.
Bergstrom
D. E.
Fang
S.
Guan
Y.
Jennings
K.
Gunaratna
N.
2006
Dyed microspheres for quantification of UV dose distributions: photochemical reactor characterization by Lagrangian actinometry
.
Journal of Environmental Engineering
132
(
11
),
1390
1403
.
Bohrerova
Z.
Bohrer
G.
Mohanraj
S.
Ducoste
J.
Linden
K. G.
2005
Experimental measurements of fluence distribution in a UV reactor using fluorescent dyed microspheres
.
Environmental Science and Technology
39
,
8925
8930
.
Boyle-Gotla
A.
Jensen
P. D.
Yap
S. D.
Pidou
M.
Wang
Y.
Batstone
D. J.
2014
Dynamic multidimensional modelling of submerged membrane bioreactor fouling
.
Journal of Membrane Science
467
,
153
161
.
Brennan
D.
2001
The numerical simulation of two-phase flows in settling tanks
.
PhD Thesis
,
University of London
,
UK
.
Burt
D. J.
2010
Improved design of settling tanks using and extended drift flux model
.
PhD Thesis
,
University of Bristol
,
UK
.
Camp
T. R.
1942
Grit chamber design
.
Sewage Works Journal
14
,
268
381
.
Camp
T. R.
1946
Sedimentation and the design of settling tanks
.
Transactions, ASCE
111
,
895
936
.
Caron
E.
Chevrefils
G.
Barbeau
B.
Payment
P.
Prevost
M.
2007
Impact of microparticles on UV disinfection of indigenous aerobic spores
.
Water Research
41
(
19
),
4546
4556
.
Dalmau
J.
Comas
J.
Rodríguez-Roda
I.
Pagilla
K.
Steyer
J. P.
2010
Model development and simulation for predicting risk of foaming in anaerobic digestion systems
.
Bioresource Technology
101
(
12
),
4306
4314
.
De Clercq
B.
2003
Computational fluid dynamics of settling tanks: development of experiments and rheological, settling and scraper submodels
.
PhD Thesis
,
Department of Applied Mathematics, Biometrics and Process Control (BIOMATH), of University of Ghent
,
Belgium
.
Ducoste
J.
Clark
M.
1998
The influence of tank size and impeller geometry on turbulent flocculation: I. Experimental
.
Environmental Engineering Science
15
(
3
),
215
224
.
Ducoste
J. J.
Linden
K. G.
Rojker
D.
Liu
D.
2005a
Assessment of reduction equivalent fluence bias using computational fluid dynamics
.
Environmental Engineering Science
22
(
5
),
615
628
.
Ekama
G. A.
Barnard
J. L.
Gunthert
F. W.
Krebs
P.
McCorquodale
J. A.
Parker
D. S.
Wahlberg
E. J.
1997
Secondary Settling Tanks: Theory, Modelling, Design and Operation
.
IAWQ
,
Scientific and Technical Report No. 6
.
Eshtiaghi
N.
Markis
F.
Yap
S. D.
Baudez
J. C.
Slatter
P.
2013
Rheological characterisation of municipal sludge: a review
.
Water Research
47
(
15
),
5493
5510
.
Ferziger
J. H.
Peric
M.
2002
Computational Methods for Fluid Dynamics
,
3rd edn.
Springer
,
Berlin, Germany
.
Fletcher
C. A. J.
1991a
Computational Techniques for Fluid Dynamics
.
Volume I, Fundamental and General Techniques
,
2nd edn
.
Springer-Verlag
,
Heidelberg, Germany
.
Fletcher
C. A. J.
1991b
Computational Techniques for Fluid Dynamics
.
Volume II, Specific Techniques for Different Flow Categories
,
2nd edn.
Springer-Verlag
,
Heidelberg, Germany
.
Gaden
D.
2013
Modelling anaerobic digesters in three dimensions: integration of biochemistry with computational fluid dynamics
.
PhD Thesis, University of Manitoba, Canada
. (
accessed 9 March 2016
).
Gong
M.
Xanthos
S.
Ramalingam
K.
Fillos
J.
Beckmann
K.
Deur
A.
McCorquodale
J. A.
2009
Development of a flocculation sub-model for a 3-D CFD model based on rectangular settling tanks
. In:
Proceedings of the Water Environment Federation
,
WEFTEC
2009, Orlando, FL, USA
.
Greene
D. J.
2002
Numerical simulation of chlorine disinfection processes in non-ideal reactors
.
PhD Thesis
,
Drexel University
,
Philadelphia, PA, USA
.
Griborio
A.
2004
Secondary clarifier modeling: a multi-process approach
.
PhD Thesis
,
University of New Orleans
,
LA, USA
. (
accessed 9 March 2016
).
Griborio
A.
McCorquodale
J. A.
2006
Optimum design of your center well: use of a CFD model to understand the balance between flocculation and improved hydrodynamics
. In:
Proceedings of the Water Environment Federation
,
WEFTEC 2006, Dallas, TX, USA: Session 1 through Session 10
, pp.
263
280
.
Griborio
A.
McCorquodale
J. A.
Rodriguez
J. A.
2014
CFD modeling of primary clarifiers: the state-of-the-art
. In:
Proceedings of the Water Environment Federation
,
WEFTEC 2014, New Orleans, LA, USA: Session 510 through Session 518
, pp.
1926
1949
.
Hassan
J. M.
Mohammed
W. S.
Mohammed
T. A.
Alawee
W. H.
2014
CFD simulation for manifold and tapered longitudinal section
.
International Journal of Emerging Technology and Advanced Engineering
4
(
2
),
28
35
.
Henze
M.
Gujer
W.
Mino
T.
van Loosdrecht
M.
2000
Activated Sludge Models ASM1, ASM2, ASM2d, and ASM3
,
IWA Scientific and Technical Report
,
London, UK
.
Imam
E.
McCorquodale
J. A.
Bewtra
J. K.
1983
Numerical modelling of sedimentation tanks
.
Journal of Hydraulic Engineering
109
(
12
),
1740
1754
.
Karpinska
A. M.
Bridgeman
J.
2016
CFD-aided modelling of activated sludge systems – A critical review
.
Water Research
88
(
10
),
861
869
.
Kinnear
D. J.
2002
Biological solids sedimentation: a model incorporating fundamental settling parameters
.
PhD Thesis
,
University of Utah
,
Salt Lake City
,
UT, USA
.
Kleine
D.
Reddy
B. D.
2005
Finite element analysis of flows in secondary settling tanks
.
International Journal for Numerical Methods in Engineering
64
,
849
876
.
Knatz
C.
2005
Modeling with CFD
.
Public Works
136
(
3
),
50
52
,
54–55
.
Krebs
P.
Armbruster
M.
Rodi
W.
1998
Laboratory experiments of buoyancy-influenced flow in clarifiers
.
Journal of Hydraulic Research
36
(
5
),
831
851
.
Lakehal
D.
Krebs
P.
Krijgsman
J.
Rodi
W.
1999
Computing shear flow and sludge blanket in secondary clarifiers
.
Journal of Hydraulic Engineering
125
(
3
),
253
262
.
Laurent
J.
Samstag
R.
Ducoste
J.
Griborio
A.
Nopens
I.
Batstone
D.
Wicks
J.
Saunders
S.
Potier
O.
2014
A protocol for the use of computational fluid dynamics as a supportive tool for wastewater treatment plant modelling
.
Water Science and Technology
70
(
10
),
1575
1584
.
Laursen
J.
2006
WWTP process tank modelling – the integration of advanced hydrodynamic and microbiological models
.
PhD Thesis
,
Aalborg University
,
Denmark
.
Le Moullec
Y.
Gentric
C.
Potier
O.
Leclerc
J.
2010b
CFD Simulation of the hydrodynamics and reactions in an activated sludge channel reactor of wastewater treatment
.
Chemical Engineering Science
65
,
492
498
.
Liu
D.
Ducoste
J. J.
Jin
S.
Linden
K.
2004
Evaluation of alternative fluence rate distribution models
.
J. Water Supply: Research & Technology – AQUA
53
(
6
),
391
408
.
Liu
D.
Ducoste
J. J.
Wu
C.
Linden
K. G.
2007
Numerical simulation of UV disinfection reactors: evaluation of alternative turbulence models
.
Applied Mathematical Modeling
31
,
1753
1769
.
Marques
N.
2015a
OpenFOAM® in wastewater applications: 7 – Hands-on: Splitter box. Watermatex 2015 Workshop: Computational Fluid Dynamics – Hands-on CFD Modeling for Water Resource Recovery Facilities
,
Gold Coast, Queensland
,
Australia
. .
Marques
N.
2015b
OpenFOAM® in wastewater applications: 5 – Hands-on: Clarifier. Watermatex 2015 Workshop: Computational Fluid Dynamics – Hands-on CFD Modeling for Water Resource Recovery Facilities
,
Gold Coast, Queensland
,
Australia
. .
Mazzolani
G.
Pirozzi
F.
D'Antonio
G.
1998
A generalized settling approach in the numerical modeling of sedimentation tanks
.
Water Science and Technology
38
(
3
),
95
102
.
McCorquodale
J. A.
Zhou
S. P.
1993
Effect of hydraulic and solids loading on clarifier performance
.
Journal of Hydraulic Research, IAHR
,
31
(
4
),
461
470
.
McCorquodale
J. A.
Yuen
E. M.
Vitasovic
Z.
Samstag
R. W.
1991
Numerical simulation of unsteady conditions in clarifiers
.
Water Pollution Research Journal of Canada
26
(
2
),
201
222
.
McNamara
B. F.
Layne
J.
Hyre
M.
Kinnear
D. J.
Bott
C. B.
2012
Evaluation of three full-scale grit removal processes using CFD modeling
. In:
Proceedings of the Water Environment Federation
,
WEFTEC 2012, New Orleans, LA, USA: Session 81 through Session 90
, pp.
6008
6030
.
Naessens
W.
Maere
T.
Ratkovich
N.
Vedantam
S.
Nopens
I.
2012
Critical review of membrane bioreactor models–Part 2: hydrodynamic and integrated models
.
Bioresource Technology
122
,
107
118
.
Nopens
I.
2005
Modelling the activated sludge flocculation process: a population balance approach
.
PhD Thesis
,
University of Ghent
,
Belgium
.
Nopens
I.
Biggs
C. A.
De Clercq
B.
Govoreanu
R.
Wilen
B. M.
Lant
P.
Vanrolleghem
P. A.
2002
Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)
.
Water Science and Technology
45
(
6
),
41
49
.
Parker
D. S.
Kaufman
W. J.
Jenkins
D.
1970
Characteristics of Biological Floc in Turbulent Regimes
.
SERL Report 70-5
.
University of California
,
Berkeley, CA, USA
.
Parker
D. S.
Kaufman
W. J.
Jenkins
D.
1971
Physical conditioning of activated sludge flocs
.
Journal Water Pollution Control Federation
43
(
9
),
1817
1834
.
Parker
D. S.
Kaufman
W. J.
Jenkins
D.
1972
Floc breakup in turbulent processes
.
Journal of the Sanitary Engineering Division, ASCE, SA1
98
(
1
),
79
99
.
Patankar
S. V.
1980
Numerical Heat Transfer and Fluid Flow
.
Hemisphere Publishing Corporation, Taylor & Francis Group
,
New York, NY
,
USA
.
Pereira
J.
Karpinska
A.
Gomes
P.
Martins
A.
Dias
M.
Santos
R.
2011
Activated Sludge Models coupled to CFD simulations
. In:
Dias
R.
Lima
R.
Martins
A. A.
Mata
T. M.
(eds),
Single and Two-Phase Flows on Chemical and Biomedical Engineering
.
Bentham Science Publishers
,
Dubai
,
UAE
.
Ratkovich
N.
2010
Understanding Hydrodynamics in Membrane Bioreactor Systems for Wastewater Treatment: Two-phase Empirical and Numerical Modelling and Experimental Validation
.
PhD Thesis
,
Faculty of Bioscience Engineering, University of Ghent
,
Belgium
.
Ratkovich
N.
Horn
W.
Helmus
F. P.
Rosenberger
S.
Naessens
W.
Nopens
I.
Bentzen
T.
2013
Activated sludge rheology: a critical review on data collection and modeling
.
Water Research
47
(
2
),
463
482
.
Rehman
U.
Maere
T.
Vesvikar
M.
Amerlinck
Y.
Nopens
I.
2014
Hydrodynamic-biokinetic model integration applied to a full-scale WWTP
. In:
IWA World Water Congress & Exhibition 2014
,
September 21–26
,
Lisbon
,
Portugal
.
Roache
P. J.
1982
Computational Fluid Dynamics
.
Hermosa Publishers
,
Albuquerque
,
NM, USA
.
Rodi
W.
2000
Turbulence Models and Their Application in Hydraulics
.
International Association for Hydraulic Research, A.A. Balkema
,
Rotterdam
,
The Netherlands
.
Saalbach
J.
Hunze
M.
2008
Flow structures in MBR-tanks
.
Water Science and Technology
57
(
5
),
699
705
.
Samstag
R. W.
Wicklein
E. A.
Reardon
R. D.
Leetch
R. J.
Parks
R. M.
Groff
C. D.
2012
Field and CFD analysis of jet aeration and mixing
. In:
Proceedings of the Water Environment Federation
,
WEFTEC 2012, New Orleans, LA, USA: Session 51 through Session 60
, pp.
4113
4139
(
27
).
Sobremisana
A. P.
Ducoste
J. J.
de los Reyes
F. L.
III
2011
Combining CFD, FLOC dynamics, and biological reaction kinetics to model carbon and nitrogen removal in an activated sludge system
. In:
Proceedings of the Water Environment Federation
,
WEFTEC 2011, Los Angeles, CA, USA: Session 51 through Session 60
, pp.
3272
3282
(11)
.
Sozzi
D. A.
Taghipour
F.
2006
UV Reactor performance modeling by Eulerian and Lagrangian methods
.
Environmental Science and Technology
40
(
5
),
1609
1615
.
Stamou
A. I.
Adams
E. W.
Rodi
W.
1989
Numerical modeling of flow and settling in primary rectangular clarifiers
.
Journal of Hydraulic Research
27
(
5
),
665
682
.
Takacs
I.
Patry
G. G.
Nolasco
D.
1991
A dynamic model of the clarification thickening process
.
Water Research
25
(
10
),
1263
1271
.
Takamatsu
T.
Naito
M.
Shiba
S.
Ueda
Y.
1974
Effects of deposit resuspension on settling basin
.
Journal of the Environmental Engineering Division, ASCE
100
(
EE4
),
883
903
.
Tchobanoglous
G.
Burton
F.
Stensel
H.
2003
Metcalf and Eddy Inc. Wastewater Engineering, Treatment and Reuse
.
McGraw-Hill
,
New York, NY,
USA
.
Tong
J. C. K.
Sparrow
E. M.
Abraham
J. P.
2009
Geometric strategies for attainment of identical outflows through all the exit ports of a distribution manifold
.
Applied Thermal Engineering
29
(
17
),
3552
3560
.
Verhoff
F. H.
Tenney
M. W.
Echelberger
W. F.
1974
Mixing in anaerobic digestion
.
Biotechnology and Bioengineering
16
(
6
),
757
770
.
Vesilind
P. A.
1968
Discussion of ‘Evaluation of activated sludge thickening theories’, by R. I. Dick and B. B. Ewing
.
Journal of the Sanitary Engineering Division, ASCE
94
,
185
191
.
Wicklein
E.
Batstone
D. J.
Ducoste
J.
Laurent
J.
Griborio
A.
Wicks
J.
Saunders
S.
Samstag
R.
Potier
O.
Nopens
I.
2016
Good modelling practice in applying computational fluid dynamics for WWTP modelling
.
Water Science and Technology
73
(
5
),
969
982
.
Wols
B.
2010
CFD in drinking water treatment
.
PhD Thesis
,
Delft University of Technology
,
Delft, The Netherlands
.
Wols
B. A.
Shao
L.
Uijttewaal
W. S. J.
Hofman
J. A. M. H.
Rietveld
L. C.
Van Dijk
J. C.
2010
Evaluation of experimental techniques to validate numerical computations of the hydraulics inside a UV bench-scale reactor
.
Chemical Engineering Science
65
(
15
),
4491
4502
.
Wu
B.
2009a
CFD Analysis of mechanical mixing in anaerobic digesters
.
Structures & Environment Division of ASABE
52
(
4
),
1371
1382
.
Wu
B.
Chen
S.
2008
CFD simulation of non-newtonian fluid flow in anaerobic digesters
.
Biotechnology and Bioengineering
99
,
700
711
.
Zhou
S.
McCorquodale
J. A.
1992a
Influence of skirt radius on performance of circular clarifier with density stratification
.
International Journal for Numerical Methods in Fluids
14
,
919
934
.
Zhou
S.
McCorquodale
J. A.
1992b
Modelling of rectangular settling tanks
.
Journal of Hydraulic Engineering
118
(
10
),
1391
1405
.
Zhou
S.
McCorquodale
J. A.
1992c
Mathematical modelling of a circular clarifier
.
Canadian Journal of Civil Engineering
19
,
365
374
.