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Thermal effects on the hydraulic performance of sedimentation ponds
Journal of Water Process Engineering 33 (2020) 101100
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Journal of Water Process Engineering journal homepage: www.elsevier.com/locate/jwpe
Thermal effects on the hydraulic performance of sedimentation ponds a,
b,c
Danial Goodarzi *, Kaveh Sookhak Lari , Farshid Mossaiby
T
d
a
Department of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran CSIRO Land and Water, Private Bag No. 5, Wembley, WA, 6913, Australia School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup, WA, 6027, Australia d Department of Civil Engineering, University of Isfahan, 81744-73441 Isfahan, Iran b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Water treatment Ponds Buoyancy Thermal driven flow Simulation
Numerous pilot and computational studies have investigated effects of inlet, outlet, baffles and geometry on the hydraulic performance of sedimentation ponds in water and wastewater treatment plants. However, no full-scale study has addressed buoyancy effects caused by variations in the ambient temperature and the real-time temperature of the fluid at the inlet. This might significantly affect the hydraulic performance of sedimentation ponds. For the first time, we conduct representative simulations to study effects of variations in the temperature on the hydraulic performance of a plant-scale rectangular pond. It is shown that even a small difference between the temperature at the inlet and the bulk flow inside the pond could augment thermal stratification, as a result of buoyancy forces. The results reveal that buoyancy forces in a typical pond would decrease the hydraulic retention time and the effective volume. We suggest that understanding the effect of temperature profiles on the hydraulic performance of ponds should be a prerequisite for improving the design and configuration.
1. Introduction
number of layouts and inlet and outlet configurations [6]. Others studied effects of modifying the layout (e.g. by applying baffles and changing inlet-outlet and geometry configurations) to improve the hydraulic performance of ponds. An example is the study by Goula et al. (2008) who simulated the effect of baffle implementation on the settling efficiency. It was shown that appropriate application of baffles in a circular settling tank could increase the settling rate of fine particles [5]. Goodarzi et al. (2018) conducted a number of simulations to address the effect of baffles on the hydraulics and settling efficiency of rectangular ponds in a windy climate [7]. Similar results and findings were reported in other studies [7–11]. However, neither of these computational studies addressed the effect of thermal stratification on the hydraulic performance of ponds. The hydrodynamics of a pond is significantly affected by characteristics of the inlet and variations in the vertical density profile of the fluid. A non-uniform temperature profile, as the major cause of stratification, is subjected to considerable fluctuations due to (e.g.) changes in the ambient conditions [12]. Temporal and spatial extent of heterogeneity in the temperature is a function of the magnitude of mixing [13,14]. Experimental studies on thermally stratified flows have demonstrated a substantial reduction in the hydraulic performance of ponds [15,16]. In a pilot study, Hendi et al. (2018) investigated buoyancydriven flows caused by temperature difference between the bulk flow
Application of appropriate treatment processes is essential to meet strict environmental and public health standards and regulations on drinking water. Turbidity is a major water quality indicator to assess efficiency of treatment processes to diminish suspended particles. Gravitational settling is the primary physical separation mechanism for solid particles. It drastically reduces chemical and biological loadings in the treated water [1,2]. The hydraulic efficiency of a sedimentation pond is affected by the geometry and configuration of the pond, as well as ambient parameters. Thermal stratification, wind flow and inappropriate hydraulic design of sedimentation ponds could increase turbulence in the flow and deteriorate the settling efficiency [3]. Hence, the hydraulic efficiency of sedimentation ponds has received considerable attention during the recent years, as one-third of the water treatment cost is consumed for separation processes [4]. Pilot and field-scale study of sedimentation basins are expensive and time demanding. On the other hand, computational fluid dynamics (CFD) methods together with advances in computing facilities (such as parallel-processing infrastructures) facilitate cost-effective prediction of fluids flow patterns and hydraulics of sedimentation ponds [5]. Computational studies on the hydraulics of ponds have mostly concentrated on the effects of physical characteristics and configuration of the ponds. In one of the most leading studies, Persson explored a ⁎
Corresponding author. E-mail address: [email protected] (D. Goodarzi).
https://doi.org/10.1016/j.jwpe.2019.101100 Received 3 September 2019; Received in revised form 6 December 2019; Accepted 7 December 2019 2214-7144/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 1. The geometry of the rectangular pond. The figure is not to scale.
Fig. 2. Mesh refinement and clustering the simulation domain of the rectangular tank.
rarely addressed the effect of temperature on the hydraulic efficiency of ponds. For the first time, we consider a real-time inflow temperature profile and temperature differences between the walls and the bulk flow to computationally study the hydraulics of a plant-scale rectangular sedimentation pond. Through applying reasonable computational resources and existing open-source codes, the possibility of optimizing the layout (to reduce stratification) is tested. The outcome of this study can help to optimize the design of sedimentation ponds.
Table 1 Boundary conditions for flow variables and the temperature. Boundary conditions Variable
Inlet
Outlet
Surface
Side walls and bottom
U p k ε νT T
fixedValue zeroGradient fixedValue fixedValue calculated codeStream
inletOutlet fixedValue zeroGradient zeroGradient calculated calculated
slip slip slip slip slip zeroGradient
noSlip zeroGradient kqRWallFunction epsilonWallFunction nutkWallFunction codedFixedValue
2. Method 2.1. The model
(inside a pond) and the inflow. The results demonstrated that thermal driven flows increase the chance of short-circuiting and deteriorate the hydraulic performance of the pond [17]. In a computational study, temperature profiles in a circular sedimentation tank were investigated. It was shown that an infinitesimal thermal difference is sufficient to generate a density-driven flow [18]. Computational and numerical studies on sedimentation ponds have
A three dimensional (3D) version of the domain reported in Alighardashi and et al. (2019) (case nw-d3) is applied [19]. This includes a rectangular sedimentation pond (typically used in water and wastewater treatment plants) with a length of 35 m, depth of 3 m and width of 3 m (Fig. 1). The total volume of the pond is 315 m3 with an inflow rate of 0.0335 [m3/s] and a nominal hydraulic retention time of 2
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 3. The applied temperature profiles on the walls and at the inlet.
numerical mesh consists of 1,041,600 hexahedron cells with refinements in the resolution near the inlet, outlet and the solid boundaries (Fig. 2). Velocity inlet, pressure outlet and no-slip wall boundary conditions were utilized for the inlet, outlet and the walls respectively. In order to reduce the computational costs of the simulations we ignored the energy exchange between the ambient air and the flow at surface. Table 1 summarizes the boundary conditions applied in this study for all the cases. Representative equations for the standard terminology used in the table can be found in OpenFOAM user guide [20]. Variables are introduced in Section 2.3. The applied temperature profiles at walls and the inlet are based on
Table 2 Temperature variation of walls and inlet. Case
Walls
Inlet
1 2 3 4
14-23 14-23 17-23 17-23
– 20-21 20-21 20-22
2.9 h. The height and width of the inlet and outlet are 0.3 m and 3 m respectively. This is a common rectangular sedimentation basin, widely used in water and wastewater treatment plants [1]. The structured
Fig. 4. Comparisons of the velocity magnitude in the simulations versus the numerical results by Alighardashi et al (2019) [19]. 3
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 5. Comparison of the velocity magnitude in the simulations versus the experimental results in Liu et al (2009) [31].
data shown in Fig. 3. We conducted the simulations on a Linux-based cluster with 16 nodes (each with 2 cores) and 32 GB of RAM. The total simulation time was 1000 CPU hours, equal to 31 h of elapsed real time (wall time). 2.2. Simulation scenarios Four simulation cases are considered to study the thermal stratification. For the first case, we only consider a temperature profile on the side walls. The constant inflow temperature is set to 20 °C. The vertical variation of the temperature on the walls is based on the soil temperature data measured at Shahid Beheshti University, as depicted in Fig. 3 (left). For the other cases, we also consider a time-dependent temperature of the inflow (Fig. 3 - right). Table 2 presents the ranges of the temperature for the inflow and the walls. 2.3. Mathematical modelling and governing equations
Fig. 6. Calculated concentration of the tracer at the outlet for the four cases.
Continuity and Reynolds averaged Navier–Stokes (RANS) equations for a single-phase fluid are applied to solve the 3D water flow in a fullscale sedimentation pond:
Table 3 Hydraulic characteristics of the pond. The unit for time is hour. Case
HRTN HRTR e ti Variance Short–circuiting
1
2.9 2.5121 0.8662 0.75 3.563 0.2986
2
2.9 2.3956 0.826 0.625 3.6519 0.2609
3
2.9 2.4389 0.841 0.639 3.6343 0.2620
4
2.9 2.4128 0.832 0.631 3.6486 0.2615
Alighardashi and et al [19]
∂ρ + ∇ . ρv = 0, ∂t
2.9 2.8378 0.9786 1.1183 2.0224 N/A
∂ ρv = −(∇ . ρvv ) − ∇p − ∇ . τ + ρg , ∂t
(1)
3
(2)
Where, ρ is density [kg/m ], v is the Reynolds-averaged velocity [m/s], t and p are time [s] and (averaged) pressure [kg/ms2], τ is the stress tensor [N/m2] and g denotes the gravitational acceleration [m/s2] [21]. The open source library, finite-volume, numerical package OpenFOAM (v6) 2018 was used to simulate water and heat transfer in the pond. OpenFOAM consist of C++ libraries and various platforms to solve fluids dynamics problems [20]. Standard k − ε closure of Jones 4
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 7. Vertical temperature profiles for all cases. The vertical axis represents the depth (m) and the horizontal axis is the temperature (oC) (time = 15 p.m.).
where μt and kt are turbulent viscosity [kg/m.s] and thermal diffusivity [kg/m.s], Pk is production of turbulent energy, Prt = 1 is the Prandtl number and constants are Cε1 = 1.44 , Cε2 = 1.92, Cμ = 0.09, σk = 2 , σε = 1.3 [21]. Fluid (here water) properties are considered as functions of temperature. Density is calculated using the Boussinesq approximation [25]:
and Launder is used to calculate eddy viscosity term in RANS equations [22]. This model has shown adequate performance to study process tanks [5,19,23,24]. In this model, turbulence viscosity μt , thermal diffusivity kt , turbulent kinetic energy k and turbulent energy dissipation rate ε are computed through solving the following coupled equations:
μt = ρCμ
kt =
k2 ε
(3)
(ρ − ρ0 ) g = −ρ0 g β(T − T0)
Cp μt
Where, ρ and ρ0 = 998.21 are density and reference density [kg/m3], β= 0.000214 denotes thermal expansion coefficient [1/K], T and T0 = 293.15 are temperature and reference temperature [K]. We used the viscosity-temperature model based on Vogel's empirical equation [26]:
(4)
Prt
μ ∂ (ρk ) + ∇ . (ρvk ) = ∇ . ⎜⎛ ⎛μ + t ⎞ ∇k ⎟⎞ + Pk − ρε σ ∂t k⎠ ⎝⎝ ⎠
(5)
μ ε ε2 ∂ (ρε ) + ∇ . (ρvε ) = ∇ . ⎜⎛ ⎛μ + t ⎞ ∇ε ⎟⎞ + Cε1 Pk − Cε 2 ρ σε ⎠ ⎠ k k ∂t ⎝⎝
(6)
⎜
⎜
(7)
⎟
νt = exp(A +
⎟
5
B ) × 10−6 T+C
(8)
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 8. Magnitude of the velocity contours for case 1 and 2 (time = 15 p.m.). ∞
Where, νt the denotes kinematic viscosity [m2/s], T is the temperature [K] and other constants for water are A = −3.7188, B= 578.919 and C= −137.546. For all of the cases, we start the simulations by assuming a given pattern for the flow field as the initial condition. The simulation of the flow field continues until the steady state condition is met, which takes a simulation time around 3.5 times of nominal hydraulic retention time. We then perform a tracer study to investigate the hydrodynamics of the pond, including the retention times and dead zones [27]. Dynamic flow method is applied in which the continuity, RANS equations and scalar transport equation are solved simultaneously at every time step. The mass transport equation is implemented in the standard solver buoyantBoussinesqPimpleFoam to approximate the solute mass transport equation [28,29].
∂c → + v . ∇c = ∇ [∇ (D + Dt ) c ] ∂t
∫ (t − HRTR )2c (t ) dt σ2 =
Finally, the hydraulic efficiency of the pond is defined as the ratio of the real and nominal hydraulic retention time:
e=
HRTR HRTN
(12)
and the short circuiting index is defined as:
Short− circuiting =
ti HRTR
(13)
Where, ti is the time that the tracer first appears at outlet, at a concentration above a given threshold.
(9) 3. Verification We first conducted a mesh sensitivity analysis with three different resolutions consist of 1,041k, 690k and 1,250k hexahedron grid cells. The velocity profiles in the sedimentation pond introduced in Alighardashi et al. (2019) [19] were simulated (the same configuration is also used to conduct the simulations in this paper). The pond is a 3 m wide, 35 m long and 3 m deep with a horizontal flow rate equal to 0.03245 m/s. More details can be found in the original study. The results (Fig. 4) show a slight different in the water velocity profile for the different meshes applied. Nevertheless, all the three
∞ 0 ∞ 0
(11)
0
∫ tc (t ) dt ∫ c (t ) dt
∞
∫ c (t ) dt
Here the tracer concentration is c [Unit mass/m3], Dt and D are turbulence and molecular diffusion coefficient [m2/s] and a turbulent Schmidt number ScT = 1 is considered [30]. The concentration of the tracer is measured at the outlet to compute the real hydraulic retention time and the variance [7,19,27]:
HRTR =
0
(10) 6
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 9. Magnitude of the velocity contours for case 3 and 4 (time = 15 p.m.).
to measure water flow field and mean velocity in a pond with 2.5 m length and 0.075 m height (case 3 in the original study). The result of our OpenFOAM simulation versus the original measurements is depicted in Fig. 5 and show good agreement. 4. Results The output from the model are text-based files including temporal and spatial values of calculated velocities, pressures, temperatures and concentrations. We processed and visualized the output files by using the open-source post-processor ParaView [32]. Below we provide the visualized data and discuss the results of the simulations. 4.1. Effect of temperature variations on HRTR For all the cases introduced in Section 2.2 the water flow was simulated in the transient mode for at least 3.5 times of hydraulic retention time (of the pond) until the velocities and pressures reached a steady state. Even for the cases with a time-dependent temperature at the inlet (cases 2–4) the final simulations start from this steady state as the initial condition. A passive scalar was then injected at the inlet (time = 8 a.m.). The total injection duration was 10 s and the concentration of the tracer in the injected volume was equal to 1 (Unit mass/m3). The width-wise averaged concentration of the tracer was continuously calculated at the outlet. Residence time distributions (RTD) plots of four cases are shown in Fig. 6.
Fig. 10. Flow streamlines for case 1 and 2 (time = 15 p.m.).
meshes produced acceptable results compared to the results in the original study. The first mesh (comprising 1,041k grid cells) were then used to simulate the four cases of this study. Second, we resembled the study in Lui et al. (2009) [31]. This is a lab scale experiment with a two-dimensional laser Doppler velocimetry 7
Journal of Water Process Engineering 33 (2020) 101100
D. Goodarzi, et al.
Fig. 11. Flow streamlines for case 3 and 4 (time = 15 p.m.).
show the magnitude of the velocity vectors for all the cases, clearly visualizing a preferential horizontal flow at the surface. This is in a good agreement with the experimental study in Hendi et al. (2018) [17]. Figs. 10 and 11also depict the flow streamlines for all the cases. It is seen that the effect of thermal stratification results in a considerable portion of the pond to behave as a dead zones. The figures also show the preferential upwards pattern of the flow filed across the pond.
Detailed analysis of the data in Fig. 6 shows that the short-circuiting problem is more augmented for cases 2–4 (compared to case 1), as also seen in Table 3 (see also Eq. 13). This is mainly due to the greater thermal stratification caused by the inlet condition and augmented by the varying wall temperatures in these cases. Fig. 6 shows that the highest maximum of concentration (at the outlet) is observed for case 2. This highlights a more pronounced stratification (or a more significant short-circuiting effect) as a result of a greater difference in the temperature profile (see also Table 2). The wider extent of the concentration profile in case 1 also represents a longer HRT in comparison to the other cases, as also reported in Table 3. Hydraulic characteristics of all the simulation cases are listed in Table 3. More visible effects on the HRT is observed for case 2. Despite the variations of the inlet temperature for this case were less than the counterpart values for cases 3 and 4, case 2 experienced a steeper temperature profile on the walls – which seems to be the dominant factor in reducing HRT. Indeed, the simultaneous interaction between the temperature profile on the walls and the temporal changes of the temperature at the inlet caused 16 % reduction in HRT for case 2, compared to the results in [18] (where no temperature differences existed). Short-circuiting is also more augmented in case 2 (the minimum value for e in Table 3) due to the greater thermal stratification.
5. Conclusions The purpose of this study was to determine the effect of ambient and inlet temperature variations on the hydraulic performance of a typical rectangular pond. The findings suggested that considering temporal and spatial variations in the temperature profiles of the flow and the boundaries might have considerable effects on understanding the hydraulic performance. The simulations here showed that including the inlet and ambient temperature profiles would reduce around 16 % of the hydraulic retention time. The buoyancy forces also led to the deterioration of the other indicators such as short circuiting. As a complementary work to the existing literature, the study showed that in addition to the inlet, outlet, baffles and wind effects, temperature variations should also be considered in optimal design and operation of water and wastewater treatment ponds. The computational approach and the resources used here shows that the representative simulations for such designs are affordable. Proper design would lead to a potential decrease to the consumption of chemicals (such as coagulants – hence less sludge formation) and improve water quality indicators, such as turbidity. Further experimental and numerical investigations to assess heat transfer at the surface, wind and sunlight effects are recommended.
4.2. Velocity and temperature profiles The simulations highlighted the effect of variations in the temperature on the formation of thermal stratification in the pond. Fig. 7 depicts the depth-wise temperature profiles at different locations of the pond for all the cases. It is observed that the difference between the ambient and inflow temperature causes a thermal stratification in the pond. There is a clear decreasing trend in the vertical differences of the temperature along the pond. Close to the inlet, the depth-wise temperature difference is about 2.5 degrees Celsius and it depletes to 1 near the outlet. This implied that thermal stratification is more pronounced at entrance of the pond. Due to the differences between the temperature of the flow at the inlet and the bulk flow in case 2–4 thermal stratification is more significant and vertical temperature gradients are greater than case 1 (Fig. 7). An increase in the temperature difference caused more buoyancy effects and disturbed the flow pattern. Figs. 8 and 9
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Journal of Water Process Engineering 33 (2020) 101100
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[14] K. Sookhak Lari, M. van Reeuwijk, Č. Maksimović, S. Sharifan, Combined bulk and wall reactions in turbulent pipe flow: decay coefficients and concentration profiles, J. Hydroinf. 13 (3) (2010) 324–333, https://doi.org/10.2166/hydro.2010.013. [15] R. Macdonald, A. Ernst, Disinfection efficiency and problems associated with maturation ponds, Water Sci. Technol. 19 (3–4) (1987) 557–567, https://doi.org/10. 2166/wst.1987.0235. [16] R. Pedahzur, A.M. Nasser, I. Dor, B. Fattal, H. Shuval, The effect of baffle installation on the performance of a single-cell stabilization pond, Water Sci. Technol. 27 (7–8) (1993) 45–52, https://doi.org/10.2166/wst.1993.0533. [17] E. Hendi, A.Y. Shamseldin, B.W. Melville, S.E. Norris, Experimental investigation of the effect of temperature differentials on hydraulic performance and flow pattern of a sediment retention pond, Water Sci. Technol. 77 (12) (2018) 2896–2906, https:// doi.org/10.2166/wst.2018.286. [18] A.M. Goula, M. Kostoglou, T.D. Karapantsios, A.I. Zouboulis, The effect of influent temperature variations in a sedimentation tank for potable water treatment—a computational fluid dynamics study, Water Res. 42 (13) (2008) 3405–3414, https://doi.org/10.1016/j.watres.2008.05.002. [19] A. Alighardashi, D. Goodarzi, Simulation of depth and wind effects on the hydraulic efficiency of sedimentation tanks, Water Environ. J. (2019), https://doi.org/10. 1111/wej.12478. [20] Open FOAM User Guide Version 6, OpenCFD Ltd., 2018, http://www.openfoam. com/docs/user/. [21] S.B. Pope, Turbulent Flows, IOP Publishing, 2001. [22] W. Jones, B.E. Launder, The prediction of laminarization with a two-equation model of turbulence, Int. J. Heat Mass Transf. 15 (2) (1972) 301–314, https://doi. org/10.1016/0017-9310(72)90076-2. [23] J. Zhang, A. Tejada-Martínez, Q. Zhang, Hydraulic efficiency in RANS of the flow in multichambered contactors, J. Hydraul. Eng. 139 (11) (2013) 1150–1157, https:// doi.org/10.1061/(ASCE)HY.1943-7900.0000777. [24] J. Zhang, A.E. Tejada-Martínez, Q. Zhang, H. Lei, Evaluating hydraulic and disinfection efficiencies of a full-scale ozone contactor using a RANS-based modeling framework, Water Res. 52 (2014) 155–167, https://doi.org/10.1016/j.watres. 2013.12.037. [25] J.H. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, Springer Science & Business Media, 2012. [26] M.L. Huber, R.A. Perkins, A. Laesecke, D.G. Friend, J.V. Sengers, M.J. Assael, I.N. Metaxa, E. Vogel, R. Mareš, K. Miyagawa, New international formulation for the viscosity of H 2 O, J. Phys. Chem. Ref. Data 38 (2) (2009) 101–125, https://doi. org/10.1063/1.3088050. [27] K. Sookhak Lari, A note on baffle orientation in long ponds, J. Environ. Inform. 21 (2) (2013), https://doi.org/10.3808/jei.201300240. [28] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, John Wiley & Sons, 2006. [29] K. Sookhak Lari, M. van Reeuwijk, Č. Maksimović, The role of geometry in rough wall turbulent mass transfer, Heat Mass Transf. 49 (8) (2013) 1191–1203, https:// doi.org/10.1007/s00231-013-1165-4. [30] M. Van Reeuwijk, K.S. Lari, Asymptotic solutions for turbulent mass transfer augmented by a first order chemical reaction, Int. J. Heat Mass Transf. 55 (23–24) (2012) 6485–6490, https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.048. [31] B. Liu, J. Ma, L. Luo, Y. Bai, S. Wang, J. Zhang, Two-dimensional LDV measurement, modeling, and optimal design of rectangular primary settling tanks, J. Environ. Eng. 136 (5) (2009) 501–507, https://doi.org/10.1061/(ASCE)EE.1943-7870.0000186. [32] J. Ahrens, B. Geveci, C. Law, Paraview: An end-user tool for large data visualization, The visualization handbook vol. 717, (2005).
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Contents lists available at ScienceDirect
Journal of Water Process Engineering journal homepage: www.elsevier.com/locate/jwpe
Thermal effects on the hydraulic performance of sedimentation ponds a,
b,c
Danial Goodarzi *, Kaveh Sookhak Lari , Farshid Mossaiby
T
d
a
Department of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran CSIRO Land and Water, Private Bag No. 5, Wembley, WA, 6913, Australia School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup, WA, 6027, Australia d Department of Civil Engineering, University of Isfahan, 81744-73441 Isfahan, Iran b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Water treatment Ponds Buoyancy Thermal driven flow Simulation
Numerous pilot and computational studies have investigated effects of inlet, outlet, baffles and geometry on the hydraulic performance of sedimentation ponds in water and wastewater treatment plants. However, no full-scale study has addressed buoyancy effects caused by variations in the ambient temperature and the real-time temperature of the fluid at the inlet. This might significantly affect the hydraulic performance of sedimentation ponds. For the first time, we conduct representative simulations to study effects of variations in the temperature on the hydraulic performance of a plant-scale rectangular pond. It is shown that even a small difference between the temperature at the inlet and the bulk flow inside the pond could augment thermal stratification, as a result of buoyancy forces. The results reveal that buoyancy forces in a typical pond would decrease the hydraulic retention time and the effective volume. We suggest that understanding the effect of temperature profiles on the hydraulic performance of ponds should be a prerequisite for improving the design and configuration.
1. Introduction
number of layouts and inlet and outlet configurations [6]. Others studied effects of modifying the layout (e.g. by applying baffles and changing inlet-outlet and geometry configurations) to improve the hydraulic performance of ponds. An example is the study by Goula et al. (2008) who simulated the effect of baffle implementation on the settling efficiency. It was shown that appropriate application of baffles in a circular settling tank could increase the settling rate of fine particles [5]. Goodarzi et al. (2018) conducted a number of simulations to address the effect of baffles on the hydraulics and settling efficiency of rectangular ponds in a windy climate [7]. Similar results and findings were reported in other studies [7–11]. However, neither of these computational studies addressed the effect of thermal stratification on the hydraulic performance of ponds. The hydrodynamics of a pond is significantly affected by characteristics of the inlet and variations in the vertical density profile of the fluid. A non-uniform temperature profile, as the major cause of stratification, is subjected to considerable fluctuations due to (e.g.) changes in the ambient conditions [12]. Temporal and spatial extent of heterogeneity in the temperature is a function of the magnitude of mixing [13,14]. Experimental studies on thermally stratified flows have demonstrated a substantial reduction in the hydraulic performance of ponds [15,16]. In a pilot study, Hendi et al. (2018) investigated buoyancydriven flows caused by temperature difference between the bulk flow
Application of appropriate treatment processes is essential to meet strict environmental and public health standards and regulations on drinking water. Turbidity is a major water quality indicator to assess efficiency of treatment processes to diminish suspended particles. Gravitational settling is the primary physical separation mechanism for solid particles. It drastically reduces chemical and biological loadings in the treated water [1,2]. The hydraulic efficiency of a sedimentation pond is affected by the geometry and configuration of the pond, as well as ambient parameters. Thermal stratification, wind flow and inappropriate hydraulic design of sedimentation ponds could increase turbulence in the flow and deteriorate the settling efficiency [3]. Hence, the hydraulic efficiency of sedimentation ponds has received considerable attention during the recent years, as one-third of the water treatment cost is consumed for separation processes [4]. Pilot and field-scale study of sedimentation basins are expensive and time demanding. On the other hand, computational fluid dynamics (CFD) methods together with advances in computing facilities (such as parallel-processing infrastructures) facilitate cost-effective prediction of fluids flow patterns and hydraulics of sedimentation ponds [5]. Computational studies on the hydraulics of ponds have mostly concentrated on the effects of physical characteristics and configuration of the ponds. In one of the most leading studies, Persson explored a ⁎
Corresponding author. E-mail address: [email protected] (D. Goodarzi).
https://doi.org/10.1016/j.jwpe.2019.101100 Received 3 September 2019; Received in revised form 6 December 2019; Accepted 7 December 2019 2214-7144/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Water Process Engineering 33 (2020) 101100
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Fig. 1. The geometry of the rectangular pond. The figure is not to scale.
Fig. 2. Mesh refinement and clustering the simulation domain of the rectangular tank.
rarely addressed the effect of temperature on the hydraulic efficiency of ponds. For the first time, we consider a real-time inflow temperature profile and temperature differences between the walls and the bulk flow to computationally study the hydraulics of a plant-scale rectangular sedimentation pond. Through applying reasonable computational resources and existing open-source codes, the possibility of optimizing the layout (to reduce stratification) is tested. The outcome of this study can help to optimize the design of sedimentation ponds.
Table 1 Boundary conditions for flow variables and the temperature. Boundary conditions Variable
Inlet
Outlet
Surface
Side walls and bottom
U p k ε νT T
fixedValue zeroGradient fixedValue fixedValue calculated codeStream
inletOutlet fixedValue zeroGradient zeroGradient calculated calculated
slip slip slip slip slip zeroGradient
noSlip zeroGradient kqRWallFunction epsilonWallFunction nutkWallFunction codedFixedValue
2. Method 2.1. The model
(inside a pond) and the inflow. The results demonstrated that thermal driven flows increase the chance of short-circuiting and deteriorate the hydraulic performance of the pond [17]. In a computational study, temperature profiles in a circular sedimentation tank were investigated. It was shown that an infinitesimal thermal difference is sufficient to generate a density-driven flow [18]. Computational and numerical studies on sedimentation ponds have
A three dimensional (3D) version of the domain reported in Alighardashi and et al. (2019) (case nw-d3) is applied [19]. This includes a rectangular sedimentation pond (typically used in water and wastewater treatment plants) with a length of 35 m, depth of 3 m and width of 3 m (Fig. 1). The total volume of the pond is 315 m3 with an inflow rate of 0.0335 [m3/s] and a nominal hydraulic retention time of 2
Journal of Water Process Engineering 33 (2020) 101100
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Fig. 3. The applied temperature profiles on the walls and at the inlet.
numerical mesh consists of 1,041,600 hexahedron cells with refinements in the resolution near the inlet, outlet and the solid boundaries (Fig. 2). Velocity inlet, pressure outlet and no-slip wall boundary conditions were utilized for the inlet, outlet and the walls respectively. In order to reduce the computational costs of the simulations we ignored the energy exchange between the ambient air and the flow at surface. Table 1 summarizes the boundary conditions applied in this study for all the cases. Representative equations for the standard terminology used in the table can be found in OpenFOAM user guide [20]. Variables are introduced in Section 2.3. The applied temperature profiles at walls and the inlet are based on
Table 2 Temperature variation of walls and inlet. Case
Walls
Inlet
1 2 3 4
14-23 14-23 17-23 17-23
– 20-21 20-21 20-22
2.9 h. The height and width of the inlet and outlet are 0.3 m and 3 m respectively. This is a common rectangular sedimentation basin, widely used in water and wastewater treatment plants [1]. The structured
Fig. 4. Comparisons of the velocity magnitude in the simulations versus the numerical results by Alighardashi et al (2019) [19]. 3
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Fig. 5. Comparison of the velocity magnitude in the simulations versus the experimental results in Liu et al (2009) [31].
data shown in Fig. 3. We conducted the simulations on a Linux-based cluster with 16 nodes (each with 2 cores) and 32 GB of RAM. The total simulation time was 1000 CPU hours, equal to 31 h of elapsed real time (wall time). 2.2. Simulation scenarios Four simulation cases are considered to study the thermal stratification. For the first case, we only consider a temperature profile on the side walls. The constant inflow temperature is set to 20 °C. The vertical variation of the temperature on the walls is based on the soil temperature data measured at Shahid Beheshti University, as depicted in Fig. 3 (left). For the other cases, we also consider a time-dependent temperature of the inflow (Fig. 3 - right). Table 2 presents the ranges of the temperature for the inflow and the walls. 2.3. Mathematical modelling and governing equations
Fig. 6. Calculated concentration of the tracer at the outlet for the four cases.
Continuity and Reynolds averaged Navier–Stokes (RANS) equations for a single-phase fluid are applied to solve the 3D water flow in a fullscale sedimentation pond:
Table 3 Hydraulic characteristics of the pond. The unit for time is hour. Case
HRTN HRTR e ti Variance Short–circuiting
1
2.9 2.5121 0.8662 0.75 3.563 0.2986
2
2.9 2.3956 0.826 0.625 3.6519 0.2609
3
2.9 2.4389 0.841 0.639 3.6343 0.2620
4
2.9 2.4128 0.832 0.631 3.6486 0.2615
Alighardashi and et al [19]
∂ρ + ∇ . ρv = 0, ∂t
2.9 2.8378 0.9786 1.1183 2.0224 N/A
∂ ρv = −(∇ . ρvv ) − ∇p − ∇ . τ + ρg , ∂t
(1)
3
(2)
Where, ρ is density [kg/m ], v is the Reynolds-averaged velocity [m/s], t and p are time [s] and (averaged) pressure [kg/ms2], τ is the stress tensor [N/m2] and g denotes the gravitational acceleration [m/s2] [21]. The open source library, finite-volume, numerical package OpenFOAM (v6) 2018 was used to simulate water and heat transfer in the pond. OpenFOAM consist of C++ libraries and various platforms to solve fluids dynamics problems [20]. Standard k − ε closure of Jones 4
Journal of Water Process Engineering 33 (2020) 101100
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Fig. 7. Vertical temperature profiles for all cases. The vertical axis represents the depth (m) and the horizontal axis is the temperature (oC) (time = 15 p.m.).
where μt and kt are turbulent viscosity [kg/m.s] and thermal diffusivity [kg/m.s], Pk is production of turbulent energy, Prt = 1 is the Prandtl number and constants are Cε1 = 1.44 , Cε2 = 1.92, Cμ = 0.09, σk = 2 , σε = 1.3 [21]. Fluid (here water) properties are considered as functions of temperature. Density is calculated using the Boussinesq approximation [25]:
and Launder is used to calculate eddy viscosity term in RANS equations [22]. This model has shown adequate performance to study process tanks [5,19,23,24]. In this model, turbulence viscosity μt , thermal diffusivity kt , turbulent kinetic energy k and turbulent energy dissipation rate ε are computed through solving the following coupled equations:
μt = ρCμ
kt =
k2 ε
(3)
(ρ − ρ0 ) g = −ρ0 g β(T − T0)
Cp μt
Where, ρ and ρ0 = 998.21 are density and reference density [kg/m3], β= 0.000214 denotes thermal expansion coefficient [1/K], T and T0 = 293.15 are temperature and reference temperature [K]. We used the viscosity-temperature model based on Vogel's empirical equation [26]:
(4)
Prt
μ ∂ (ρk ) + ∇ . (ρvk ) = ∇ . ⎜⎛ ⎛μ + t ⎞ ∇k ⎟⎞ + Pk − ρε σ ∂t k⎠ ⎝⎝ ⎠
(5)
μ ε ε2 ∂ (ρε ) + ∇ . (ρvε ) = ∇ . ⎜⎛ ⎛μ + t ⎞ ∇ε ⎟⎞ + Cε1 Pk − Cε 2 ρ σε ⎠ ⎠ k k ∂t ⎝⎝
(6)
⎜
⎜
(7)
⎟
νt = exp(A +
⎟
5
B ) × 10−6 T+C
(8)
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Fig. 8. Magnitude of the velocity contours for case 1 and 2 (time = 15 p.m.). ∞
Where, νt the denotes kinematic viscosity [m2/s], T is the temperature [K] and other constants for water are A = −3.7188, B= 578.919 and C= −137.546. For all of the cases, we start the simulations by assuming a given pattern for the flow field as the initial condition. The simulation of the flow field continues until the steady state condition is met, which takes a simulation time around 3.5 times of nominal hydraulic retention time. We then perform a tracer study to investigate the hydrodynamics of the pond, including the retention times and dead zones [27]. Dynamic flow method is applied in which the continuity, RANS equations and scalar transport equation are solved simultaneously at every time step. The mass transport equation is implemented in the standard solver buoyantBoussinesqPimpleFoam to approximate the solute mass transport equation [28,29].
∂c → + v . ∇c = ∇ [∇ (D + Dt ) c ] ∂t
∫ (t − HRTR )2c (t ) dt σ2 =
Finally, the hydraulic efficiency of the pond is defined as the ratio of the real and nominal hydraulic retention time:
e=
HRTR HRTN
(12)
and the short circuiting index is defined as:
Short− circuiting =
ti HRTR
(13)
Where, ti is the time that the tracer first appears at outlet, at a concentration above a given threshold.
(9) 3. Verification We first conducted a mesh sensitivity analysis with three different resolutions consist of 1,041k, 690k and 1,250k hexahedron grid cells. The velocity profiles in the sedimentation pond introduced in Alighardashi et al. (2019) [19] were simulated (the same configuration is also used to conduct the simulations in this paper). The pond is a 3 m wide, 35 m long and 3 m deep with a horizontal flow rate equal to 0.03245 m/s. More details can be found in the original study. The results (Fig. 4) show a slight different in the water velocity profile for the different meshes applied. Nevertheless, all the three
∞ 0 ∞ 0
(11)
0
∫ tc (t ) dt ∫ c (t ) dt
∞
∫ c (t ) dt
Here the tracer concentration is c [Unit mass/m3], Dt and D are turbulence and molecular diffusion coefficient [m2/s] and a turbulent Schmidt number ScT = 1 is considered [30]. The concentration of the tracer is measured at the outlet to compute the real hydraulic retention time and the variance [7,19,27]:
HRTR =
0
(10) 6
Journal of Water Process Engineering 33 (2020) 101100
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Fig. 9. Magnitude of the velocity contours for case 3 and 4 (time = 15 p.m.).
to measure water flow field and mean velocity in a pond with 2.5 m length and 0.075 m height (case 3 in the original study). The result of our OpenFOAM simulation versus the original measurements is depicted in Fig. 5 and show good agreement. 4. Results The output from the model are text-based files including temporal and spatial values of calculated velocities, pressures, temperatures and concentrations. We processed and visualized the output files by using the open-source post-processor ParaView [32]. Below we provide the visualized data and discuss the results of the simulations. 4.1. Effect of temperature variations on HRTR For all the cases introduced in Section 2.2 the water flow was simulated in the transient mode for at least 3.5 times of hydraulic retention time (of the pond) until the velocities and pressures reached a steady state. Even for the cases with a time-dependent temperature at the inlet (cases 2–4) the final simulations start from this steady state as the initial condition. A passive scalar was then injected at the inlet (time = 8 a.m.). The total injection duration was 10 s and the concentration of the tracer in the injected volume was equal to 1 (Unit mass/m3). The width-wise averaged concentration of the tracer was continuously calculated at the outlet. Residence time distributions (RTD) plots of four cases are shown in Fig. 6.
Fig. 10. Flow streamlines for case 1 and 2 (time = 15 p.m.).
meshes produced acceptable results compared to the results in the original study. The first mesh (comprising 1,041k grid cells) were then used to simulate the four cases of this study. Second, we resembled the study in Lui et al. (2009) [31]. This is a lab scale experiment with a two-dimensional laser Doppler velocimetry 7
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Fig. 11. Flow streamlines for case 3 and 4 (time = 15 p.m.).
show the magnitude of the velocity vectors for all the cases, clearly visualizing a preferential horizontal flow at the surface. This is in a good agreement with the experimental study in Hendi et al. (2018) [17]. Figs. 10 and 11also depict the flow streamlines for all the cases. It is seen that the effect of thermal stratification results in a considerable portion of the pond to behave as a dead zones. The figures also show the preferential upwards pattern of the flow filed across the pond.
Detailed analysis of the data in Fig. 6 shows that the short-circuiting problem is more augmented for cases 2–4 (compared to case 1), as also seen in Table 3 (see also Eq. 13). This is mainly due to the greater thermal stratification caused by the inlet condition and augmented by the varying wall temperatures in these cases. Fig. 6 shows that the highest maximum of concentration (at the outlet) is observed for case 2. This highlights a more pronounced stratification (or a more significant short-circuiting effect) as a result of a greater difference in the temperature profile (see also Table 2). The wider extent of the concentration profile in case 1 also represents a longer HRT in comparison to the other cases, as also reported in Table 3. Hydraulic characteristics of all the simulation cases are listed in Table 3. More visible effects on the HRT is observed for case 2. Despite the variations of the inlet temperature for this case were less than the counterpart values for cases 3 and 4, case 2 experienced a steeper temperature profile on the walls – which seems to be the dominant factor in reducing HRT. Indeed, the simultaneous interaction between the temperature profile on the walls and the temporal changes of the temperature at the inlet caused 16 % reduction in HRT for case 2, compared to the results in [18] (where no temperature differences existed). Short-circuiting is also more augmented in case 2 (the minimum value for e in Table 3) due to the greater thermal stratification.
5. Conclusions The purpose of this study was to determine the effect of ambient and inlet temperature variations on the hydraulic performance of a typical rectangular pond. The findings suggested that considering temporal and spatial variations in the temperature profiles of the flow and the boundaries might have considerable effects on understanding the hydraulic performance. The simulations here showed that including the inlet and ambient temperature profiles would reduce around 16 % of the hydraulic retention time. The buoyancy forces also led to the deterioration of the other indicators such as short circuiting. As a complementary work to the existing literature, the study showed that in addition to the inlet, outlet, baffles and wind effects, temperature variations should also be considered in optimal design and operation of water and wastewater treatment ponds. The computational approach and the resources used here shows that the representative simulations for such designs are affordable. Proper design would lead to a potential decrease to the consumption of chemicals (such as coagulants – hence less sludge formation) and improve water quality indicators, such as turbidity. Further experimental and numerical investigations to assess heat transfer at the surface, wind and sunlight effects are recommended.
4.2. Velocity and temperature profiles The simulations highlighted the effect of variations in the temperature on the formation of thermal stratification in the pond. Fig. 7 depicts the depth-wise temperature profiles at different locations of the pond for all the cases. It is observed that the difference between the ambient and inflow temperature causes a thermal stratification in the pond. There is a clear decreasing trend in the vertical differences of the temperature along the pond. Close to the inlet, the depth-wise temperature difference is about 2.5 degrees Celsius and it depletes to 1 near the outlet. This implied that thermal stratification is more pronounced at entrance of the pond. Due to the differences between the temperature of the flow at the inlet and the bulk flow in case 2–4 thermal stratification is more significant and vertical temperature gradients are greater than case 1 (Fig. 7). An increase in the temperature difference caused more buoyancy effects and disturbed the flow pattern. Figs. 8 and 9
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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