VALIDATION OF A CFD MODEL IN RECTANGULAR SETTLING TANKS

Proceedings of the 13 th International Conference on Environmental Science and Technology Athens, Greece, 5-7 September 2013 VALIDATION OF A CFD MODEL IN RECTANGULAR SETTLING TANKS A. GKESOULI 1, A. I.STAMOU 1, M. XANTHAKI 2 and S. GEORGIADIS 2 1 School of Civil Engineering, Department of Water Resources and Environmental Engineering, National Technical University of Athens, Iroon Polytechniou 5, 15780 Athens, Greece. 2 E.Y.D.A.P. S.A., Oropou 156, 11146 Athens, Greece. e-mail: gkesouli@central.ntua.gr EXTENDED ABSTRACT Sedimentation is one of the most important treatment processes in conventional Water Treatment Plants and it is performed in settling tanks, whose investment in treatment plants usually accounts for the one third of the total investment; a significant percentage of suspended solids settles by gravity and therefore, influences the degree of treatment in the downstream units and the removal efficiency of the plant. Subsequently, the determination of the removal efficiency of a sedimentation tank has been the subject of numerous theoretical and experimental studies. The removal efficiency depends on the physical characteristics of the suspended solids, as well as on the flow field and the mixing regime in the tank. Flow field and mixing can strongly affect the settling efficiency through flocculation, breakup or re-entrainment of solid particles. Therefore, the determination of the flow field and mixing characteristics, which can be determined with the use of simple or sophisticated mathematical models, is essential for the prediction of the tank efficiency. Since the flow in settling tanks is fully turbulent, in sophisticated mathematical models, a turbulence model is usually employed for the determination of the eddy viscosity and the description of turbulent mixing. In addition to turbulent mixing, large-scale mixing occurs in zones with flow recirculation, which are present even at the simplest settling tank geometries. It is obvious that simple models ignore these zones and therefore are inadequate in predicting even approximately the flow and mixing in settling tanks. The validity of a mathematical model for settling tanks can be checked by comparison with experimental data that may include flow velocity profiles, streamline patterns, size of recirculation regions, dispersion or flow-through curves, profiles of concentration of suspended solids and removal efficiencies. In the present work a Computational Fluid Dynamics model was formulated, calibrated and applied in the settling tanks of the old unit of the Water Treatment Plant of Aharnes of EYDAP SA in Attica. Calculations showed that (1) flow fields are 3-D and complex, especially in the region of the inlet of the tank, with three large recirculation areas, and (2) concentration fields depend strongly on the flow fields. In the recirculation areas (where mixing is intense) the concentrations are uniformly distributed; moreover, with increasing flow rate the suspended solids iso-concentration lines are shifted to the right (towards the outlet of the tank), the outlet concentration increases and the efficiency of the tank is reduced. The model was calibrated and verified successfully using experimentally determined removal efficiency values. Keywords: settling tank, water treatment plant, CFD modeling, suspended solids, removal efficiency 1. INTRODUCTION Sedimentation is one of the most important treatment processes in conventional Water Treatment Plants; a significant percentage of suspended solids, which is formed by the aggregation of particles in the untreated water with flocculants, settles by gravity and

therefore, influences the degree of treatment in the downstream units (usually filtration and disinfection) and the removal efficiency of the plant. Sedimentation is performed in settling tanks, whose investment in treatment plants usually accounts for the one third of the total investment. Subsequently, the determination of the removal efficiency of a sedimentation tank has been the subject of numerous theoretical and experimental studies. The removal efficiency depends on the physical characteristics of the suspended solids (e.g. particle size, density and settling velocity), as well as on the flow field and the mixing regime in the tank. Flow field and mixing can strongly affect the settling efficiency through flocculation (Lyn et al., 1992), breakup or re-entrainment of solid particles. Therefore, the determination of flow and mixing characteristics is essential for the prediction of the tank efficiency (Stamou et al., 2009). Flow and mixing characteristics can be determined with the use of mathematical models. A mathematical model can be simple (Stamou et al., 2008) or sophisticated (Stamou et al., 2000); for example in a simple model a prescribed shape (logarithmic, uniform, parabolic) for velocity that is based on a set of mean flow equations, which are solved numerically, can be adopted. Since the flow in settling tanks is fully turbulent, a turbulence model is usually employed for the determination of eddy viscosity and the description of turbulent mixing (Stamou, 1991). In addition to turbulent (small scale) mixing, large-scale (and usually intense) mixing occurs in zones with flow recirculation, which are present even at the simplest settling tank geometries with inlet baffles; see for example Krebs et al. (1996) and Stamou (1994). It is obvious that simple models ignore these zones and therefore are inadequate in predicting even approximately the flow and mixing in settling tanks. The validity of a mathematical model for settling tanks can be checked by comparison with experimental data (Stamou, 2007); these data may include flow velocity profiles, streamline patterns, size of recirculation regions, dispersion or flow-through curves (Stamou and Noutsopoulos, 1994), profiles of concentration of suspended solids (Stamou et al., 1989) and removal efficiencies (Stamou et al., 1989). In 2011 a research project was initiated at the NTUA aiming at proposing measures for the settling tanks of the Water Treatment Plant of Aharnes (WTPA) of EYDAP SA in Attica, including the use of deflectors, that are expected to reduce the detrimental effect of wind on the settling efficiency of the tanks, improve their hydrodynamic conditions and their efficiency, and thus reduce the cost of treatment. The investigation was performed with the use of a mathematical Computational Fluid Dynamics (CFD) model (Stamou, 2006) that was formulated, calibrated and applied in the settling tanks. The present paper demonstrates briefly the first part of this investigation, which is the calibration and the verification of the model, which was performed with experimental data that were obtained during the project. 2. CHARACTERISTICS OF THE SETTLING TANKS There are sixteen rectangular settling tanks in the "old unit" of the WTPA with the following dimensions: width w=14.4 m, length L=73.2 m and average water depth H=3.5 m; the design flow rate to each tank ranges from 0.25 m 3 /s to 0.31 m 3 /s. The water enters into the settling tank from the flocculation tank via four rectangular openings and exits the tank via a series of V-notch weirs installed at the outlet channels. The suspended solids at the inlet were divided into four classes, whose characteristic diameters were determined (APHA, AWWA and WEF, 2005) equal to 41 μm, 17 μm, 9.5 μm and 5 μm; for each class the settling velocity (V set) was calculated using the Stokes Law. The turbidity of the water at the inlet of the tank ranges from 2.0 to 20.0 NTU and the daily average value is calculated equal to 5.0 NTU; these turbidity values correspond to a range of concentrations of suspended solids from 2.5 mg/l to 29.4 mg/l and an average value equal to S in=7.0 mg/l. Correspondingly, the turbidity measurements at the outlet of the tank range from 0.4 to 3.8 NTU and the daily average value is equal to 1.4

NTU; the corresponding concentration values for the range and average are 0.2-5.2 mg/l and S out=1.6 mg/l, respectively. Using the average concentration values, the average removal efficiency of the tank is calculated equal to R = (5.0-1.4)/5.0 = 72 %. 3. MATHEMATICAL MODEL 3.1. Equations of the model For the calculation of the 3-D flow and solids concentration fields in the settling tank the equations of continuity, momentum and mass conservation for the solids are solved; these equations are written as follows,: U j = 0 x j (1) Ui UU j i P Ui + = - + ( RTS) + gi t x j xi x j x j (2) S Uj Vset S S + = ( TSS) (3) t x j x j x j where ρ is the density of water, U i and U j are the flow velocities in i and j direction, respectively, x i and x j are the Cartesian coordinates in i and j direction, respectively, t is the time, P is the pressure, μ is the molecular viscosity of the water, g i is the acceleration of gravity and S is the local concentration of suspended solids. The process of settling is modeled as a mass flux of solids in the direction of gravity with a settling velocity equal to V set; this flux that is proportional to V set S is added to the transport term of equation (3). For the calculation of the Reynolds (turbulent) stresses (RTS), the assumption of the isotropic turbulence is applied combined with the Bussinesq approximation, i.e. U x U i j RTS = t( + ) - k j i 3 where μ t is the eddy viscosity, δ ij is the Kronecker delta (δ ij=1 for i=j and δ ij=0 for ij ) and k is the average turbulent kinetic energy per unit mass, given by: 1 2 k = ( U i' ) (5) 2 where U i' 2 are the normal Reynolds stresses in i direction. Similarly, the Turbulent SS Stresses (TSS) are calculated by equation (6). t S TSS (6) S x j where σ s is the turbulent Schmidt number for the solids. In the present work, turbulence is modeled with the Shear Stress Transport (SST) k-ω based model (Menter, 1994). This model combines the standard k-ε model (Rodi, 1980) and the k-ω model (Wilcox, 1988); virtually, it is a transformation of the k-ε to a k-ω formulation and a subsequent addition of certain equations. The standard k-ω model (Wilcox, 1988) relates the eddy viscosity to k and to the turbulence frequency (ω). x 2 ij (4) k t = The k and ω are calculated from the following model transport equations: (7)

k U k k t x x x j t ' + = ( ) + G - k j j k j (8) Uj t 2 + = ( ) + G - (9) t x j x j x j k The standard values of the constants of the SST model are β =0.09, α=5/9 and β=3/40, the turbulent Schmidt numbers for k and ω are σ k=2 and σ ω=2, respectively, and G is the production rate of turbulence. 3.2. Numerical code Calculations were performed with the 3-D CFD code CFX 14.0 that uses the finite volume method for the spatial discretisation of the domain (http://www.ansys.com). Equations (1), (2), (3), (8) and (9) are integrated over each control volume, such that the relevant quantity (mass, momentum, S, k and ω) is conserved, in a discrete sense, for each control volume. For the continuity equation (pressure-velocity coupling) a second order central difference approximation is used, modified by a fourth order derivative in pressure, which redistributes the influence of pressure. The second order upwind Euler scheme approximates the transient term. The code employs an automatic, unstructured hybrid element mesh generator with an adaptive mesh refinement algorithm, which permits a very accurate representation of the boundaries. The advantage of using unstructured mesh is the minimization of numerical errors and the consistency of the solution throughout the domain. For the solution of the equations, a scalable and fully implicit coupled solver is used. 4. CALCULATIONS 4.1. Scenarios Calculations were performed for three scenarios with the characteristics that are shown in Table 1; these scenarios were chosen to cover the expected flow rates (Q). Initially, it was assumed that there was no flow or suspended solids in the computational domain (cold start). Transient calculations were run to steady state. Scenario Flow rate Q (m 3 /s) Table 1: Characteristics of the scenarios. Inlet velocity U in (m/s) Mean flow velocity U m (m/s) Theoretical hydraulic time Θ (h) Overflow rate OR (m/h) S1 0.25 0.119 0.0050 4.08 0.85 S2 0.28 0.134 0.0056 3.62 0.96 S3 0.31 0.149 0.0062 3.26 1.07 4.2. Numerical grid and boundary conditions The numerical grid that consisted of 126554 elements is shown in Figure 1 together with the division of the computational domain into four volumes: inlet, main domain, change of geometry and outlet, with different grid properties. The boundary conditions employed in the model are summarized in Table 2.

Figure 1. View of the numerical grid. Location Surface Bottom Walls Symmetry plane Inlet Outlet Table 2: Boundary conditions. Boundary condition Free Slip Wall - No deposition No slip wall - Smooth wall - Deposition No slip wall - Smooth wall - No deposition Symmetry Normal speed = mean inlet velocity Opening - Entrainment (Inlet flow rate = Outlet flow rate) 4.3. Flow field In Figures 2 and 3 the streamlines of the flow field at a plane xy at z = 4 m and the eddies-recirculation areas that are formed in the tank are shown, respectively. Figures 2 and 3 depict that the flow field is 3-D and complex, especially in the region of the inlet of the tank. Three main recirculation areas are observed. The first (R1) is counter-clockwise and is created above the horizontal plane of the inlet jets (y=0.55 m); R1 starts from x=5.0 m and has a length that ranges from 20.0 m (near the symmetry plane) to 40.0 m (near the wall of the tank); this length decreases with increasing flow rate. The second recirculation area (R2) is clockwise (around axis y) and its size increases with increasing flow rate, while the third (R3) is developed near the boundary wall due to the interaction of R1 and R2 with the boundary walls and has a length of approximately 10.0 m. (a) Scenario S1; flow rate Q=0.25 m 3 /s (b) Scenario S2; flow rate Q=0.28 m 3 /s (c) Scenario S3; flow rate Q=0.31 m 3 /s Figure 2. Calculated flow streamlines.

(a) Recirculation area (R1) at z=4.0 m from the boundary wall (b) Recirculation area (R2) at y=0.7 m from the bottom (c) Recirculation area (R3) at z=0.5 m from the boundary wall Figure 3. Main recirculation areas that are formed in the flow field. 4.4. Concentration field of suspended solids The suspended solids iso-concentration contours of Figure 4, which are plotted at the same planes with the flow field plots of Figure 2, show that the concentration fields depend strongly on the flow fields. In the three recirculation areas, where mixing is intense, the concentration profiles are approximately uniform. As expected, with increasing flow rate the iso-concentration lines are shifted to the right (towards the outlet of the tank), the outlet concentration increases and the efficiency of the tank is reduced. (a) Scenario S1; flow rate Q=0.25 m 3 /s (b) Scenario S2; flow rate Q=0.28 m 3 /s (c) Scenario S3; flow rate Q=0.31 m 3 /s Figure 4. Iso-concentration contours of suspended solids. 4.5. Calibration and verification of the model For the calibration of the model the calculated removal efficiency was compared with the experimentally determined efficiency for the flow rate Q=0.27 m 3 /s; model calibration involved the determination of the value of the percentage of the second class of suspended solids for which the calculated by the model removal efficiency coincides with the experimentally determined value (71%). This procedure, which is summarized in Table 3, was performed to take indirectly into account the effect of intense coagulation that occurs in the region of inlet of the settling tank (presence of recirculation areas with favorable velocity gradients), which is not accounted for by the mathematical model. The value of the percentage of the second class of suspended solids was determined equal to 36%. Then, using this value the verification of the model was performed; the model was applied for a flow rate equal to Q=0.31 m 3 /s to determine the removal efficiency of the tank, as shown in Table 4; the calculated efficiency 67 % coincides with the experimental value, thus proving the successful validation of the model.

In Tables 3 and 4, the efficiencies for ideal settling (Hendricks, 2011) are shown, respectively, these were found equal to 84% and 80%, i.e. they are significantly higher (by 13%) than the real tank efficiencies and set the upper theoretical limits of the removal efficiency. Table 3: Summary of the calculation of the efficiency of the tank for Q=0.27 m 3 /s (calibration of the model). Class Percentage at inlet S in (mg/l) S out (mg/l) Efficiency V set (m/h) Efficiency of ideal settling 1 45 3.166 0.009 100 5.80 100 2 36 2.526 0.885 65 0.96 100 3 4 0.274 0.196 28 0.31 34 4 15 1.050 0.945 10 0.09 10 Total 100 7.016 2.036 71-84 Table 4: Summary of the calculation of the efficiency of the tank for Q=0.31 m 3 /s (verification of the model). Class Percentage at inlet S in (mg/l) S out (mg/l) Efficiency V set (m/h) Efficiency of ideal settling 1 45 3.166 0.032 99 5.80 100 2 36 2.526 1.086 57 0.96 90 3 4 0.274 0.206 25 0.31 29 4 15 1.050 0.959 9 0.09 9 Total 100 7.016 2.282 67-80 5. CONCLUSIONS A Computational Fluid Dynamics model was formulated, calibrated and applied in the settling tanks of the old unit of the Water Treatment Plant of Aharnes of EYDAP SA in Attica. Calculations showed that (1) flow fields are 3-D and complex, especially in the region of the inlet of the tank, with three large recirculation areas, and (2) concentration fields depend strongly on the flow fields. In the recirculation areas (where mixing is intense) the concentrations are uniformly distributed; moreover, with increasing flow rate the suspended solids iso-concentration lines are shifted to the right (towards the outlet of the tank), the outlet concentration increases and the efficiency of the tank is reduced. The model was calibrated and verified successfully using experimentally determined removal efficiency values. ACKNOWLEDGEMENT The present work was performed in the NTUA within the framework of the research program entitled "Improving the efficiency of settling tanks of the Water Treatment Plant of EYDAP SA in Aharnes using mathematical models. REFERENCES 1. ANSYS-CFX, Release 14.0, URL: http://www.ansys.com (accessed 10/03/2013). 2. APHA, AWWA and WEF. (2005), Standard Methods for the Examination of Water and Wastewater, 21st ed. American Public Health Association, Washington, D.C.

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