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Numerical Analysis of Solid-Liquid Two-Phase Flow on Sandstone Wastewater of Hydropower Stations in a Rectangular Sedimentation Tank X. Ling Wang,*,† Tao Li,‡ Jian Lang,§ S. Sha Zhou,‡ L. Liang Zhang,§ and M. Xi Chen§ School of CiVil Engineering, and School of EnVironmental Science and Engineering, Tianjin UniVersity, Tianjin 300072, China, and Chengdu Hydroelectric InVestigation & Design Institute of SPC, Chengdu 610072, China
The lack of knowledge on water flow and particle behavior of sandstone wastewater in sedimentation tanks of hydropower stations is a significant challenge for the design of these processes. In this study, the Euler-Lagrange two-phase model was applied to study the flow, sedimentation, and particle trajectories in a two-stage rectangular tank that is divided into two sections with different hydraulic retention times. The interfacial momentum transfer, buoyant force, and the collision force were considered, and the Lagrange approach was employed to determine the particle trajectories of the particles. The flow patterns, removal efficiency of the particles, and particle trajectories along the tank were investigated. The experimental and numerical results revealed that the two-stage rectangular tank is efficient in dealing with high turbidity sandstone wastewater. In addition, the simulated removal efficiencies were in good agreement with the experimental results. Last, the sensitivity of particle behavior to the collision force was studied, and the effect of the baffle length on particle settling in the rectangular sedimentation tank was evaluated. 1. Introduction High turbidity wastewater is produced during the processing of sandstone aggregates in powerhouses and can result in environmental pollution and channel deposition. Without treatment, the effluent can affect the downstream water quality, add silt to stream, and elevate the riverbed. Therefore, it is imperative to treat sandstone wastewater to protect the quality of receiving water. The maximum suspended solid (SS) concentration in wastewater is 70 000 mg/L,1 and the disposal of sandstone wastewater is difficult. Moreover, there are many obstacles associated with sludge silting in sedimentation tanks and sludge dewatering in normal wastewater treatment processes that must be overcome. Because of the high sand content coupled with sludge accumulation, a reliable and mature technology for the treatment of sandstone wastewater has not yet been developed.2 Rectangular sedimentation tanks are widely used for the removal of sediment due to their simple structure and flexible operating conditions. In the present study, a modified rectangular sedimentation tank was divided into two stages by an inserting plate was developed. Each stage of the treatment processed a different hydraulic retention time (HRT); as a result, particles with different sizes were removed in each stage of the tank. Specifically, large particles settled in the first-stage tank, while small particles settled in the second-stage tank. With the rapid development of computer technology, computational fluid dynamics (CFD) has become an efficient and economical tool for the design of sedimentation tanks. Larsen3 first applied a CFD model to simulate rectangular clarifiers and demonstrated that a pycnocline was present in the basin, causing the incoming fluid to sink to the bottom of the tank soon after entering. Shamber and Larock4 used a finite volume method to solve the Navier-Stokes equations and applied k-ε model and * To whom correspondence should be addressed. Tel.: +86 02227890910. E-mail:
[email protected]. † School of Civil Engineering, Tianjin University. ‡ School of Environmental Science and Engineering, Tianjin University. § Chengdu Hydroelectric Investigation & Design Institute of SPC.
a solid concentration equation to predict the flow pattern in a rectangular basin. Long et al.5 studied the flow dynamics in a secondary sedimentation tank and modeled the solid-liquid twophase turbulent flow with a three-dimensional two-fluid model. Wang et al.6 developed a 3D computational fluid dynamics model for rectangular tanks in wastewater treatment plants that described the dynamic settling process of sludge. Circular sedimentation tanks have been studied by Goula et al.7 They studied circular sedimentation via CFD simulations to assess the effect of adding a vertical baffle at the feed section of a full-scale circular sedimentation tank and to the settling of solids in the treatment of potable water. Furthermore, Heath and Koh8 incorporated a population balance model into CFD code to model particle aggregation in solid-liquid separation systems. McCorquodale and Zhou9 modeled a two-dimensional circular clarifier with a flow model that described the velocity and turbulent viscosity field (unsteady, turbulent, density stratified flow) as well as a suspended sediment transport model to determine the particle concentration field. The aforementioned studies focused primarily on the urban water and wastewater treatment; however, wet weather wastewater treatment methods have also been modeled successfully. Harwood and Saul10 presented the advantages of CFD particle tracking in combined sewer overflow chambers and found that CFD was as a viable alternative to physical modeling. Dufresne et al.11 used the Fluent CFD code to investigate particle behavior in combined sewer detention tanks and applied the particle tracking software to analyze the effect of bed shear stress (BSS) and bed turbulent kinetic energy (BTKE) boundary conditions on the particle tracking. CFD simulations have also been used to analyze the sediment transport of multiple sediment sizes and estimate the efficiency of solids removal in a raceway. Thus, CFD simulations can provide information on the distribution and flow of particles, as well as the proportion of settled solids,12 which can be used to estimate the efficiency of the entire process. Although CFD models have been used to investigate various wastewater treatment processes, few studies have focused on high turbidity sandstone wastewater treatment in hydropower
10.1021/ie901993t 2010 American Chemical Society Published on Web 10/12/2010
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stations, and the Eulerian-Lagrangian two-phase flow model has rarely been applied to simulate turbidity wastewater. Because of the difficulties associated with high turbidity sandstone wastewater treatment, a new treatment method must be developed, and particle behavior under high turbidity conditions must be better understood. In this article, a two-stage rectangular sedimentation tank was developed for the treatment of high turbidity sandstone wastewater treatment in powerhouses. A Eulerian-Lagrangian twophase flow model was applied, and the 3D velocity and trajectory of the particles in the sludge settling was investigated. The present study, interactions between the solid and liquid phases, was considered, as well as the sensitivity of the particles to collisions. Furthermore, the effect of baffle length on particle settling in the rectangular sedimentation tank was determined. 2. Model Description Numerical schemes based on mathematical models of separated particulate multiphase flow have used a continuum approach for the fluid phase and a Lagrangian approach for the particles.13 For a 3D turbulent flow of an incompressible Newtonian fluid, the governing unsteady Eulerian equations coupled with the k-ε model are the flow equations. The velocity of the flow is obtained by solving the continuity and momentum equations of the system. For the solid phase, the trajectory of each particle can be obtained by solving the force balance equation, which includes the drag force, buoyancy force, interaction force, collision force, etc. 2.1. Governing Equations. 2.1.1. Liquid-Phase Modeling. The equations that govern the 3D turbulent flow of an incompressible Newtonian fluid are unsteady Eulerian equations coupled to the k-ε model and are partial differential equations that describe the conservation of mass and momentum. In Cartesian coordinates, the following equations govern 3D turbulent flow: (1) Continuity equation: ∂ F + ∇ · (Flul) ) 0 ∂t l
(1)
(2) Momentum equation: ∂ (F u ) + ∇ · (Flulul) ) -∇p + Flg + ∇ · (τl + τtl) + Fls ∂t l l (2) where t is the time (s), p is the piezometric pressure (Pa), gi is the gravitational acceleration (m/s2), Fl and Fs (kg/m3) are the density of the fluid and solid, respectively; Fls is the force exerted to the fluid by the particles (N/m3) (Fls ) -(Fs)/(τrs)(Us - Ul)), τrs is the average relaxation time of the particles (s) (τrs ) (ds2Fs)/ (18 µ)(1 + (1)/(6)Re2/3)-1), µ is the molecular dynamic viscosity of the fluid (N · s/m2), and Re is the relative Reynolds number (Re ) (Flds|ul - us|)/(µ)). (3) k-ε model: The k-ε model used in this study is appropriate for fully turbulent, incompressible flows and accounts for buoyancy effects. The detailed equations are provided in the literature.14-16 2.1.2. Solid-Phase Modeling: Particle Tracking. The momentum equation of computational particles was derived from Newton’s second law, and the trajectory of the particles was calculated by integrating the force balance equation: Fs
dUs ) dt
∑F
(3)
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where Us is the parcel instantaneous velocity (m s ), and ∑F is the resultant force on the particles, which can be written as
∑F ) F
D
+ g(Fs - Fl) + Fsl + Fss + Fx
(4)
The first term on the right-hand side of the equation is the interphase drag force per unit of particle mass, FD, which includes a mean and a fluctuating component, of which the latter accounts for the additional drag due to interaction between the dispersed phase and the surrounding turbulent eddies. FD can be calculated from eq 5. 1 FD ) - CdFsAd |Ul - Us |(Ul - Us) 2
(5)
where Cd is the drag coefficient and is often set to 0.5, Ad is the particles’ cross-sectional area of the particles (Ad ) (πds2)/ (4)(m2)), ds is the diameter of the particles (m), and Ul and Us are the instantaneous velocity of the fluid and solid, respectively. The second term on the right-hand side of eq 4 is the buoyancy force. Fsl is a collision force between solid and liquid (N/m3) and can be obtained from the expression: Fsl ) (Fs)/ (τrs)(us - ul). Because the sandstone concentration of sandstone is high, the collision force among particles, Fss, should be considered. Fss can be calculated from eq 6.17-19 Fss ) 2(1 + e)∇(RsFs〈c′2 p 〉)
(6)
where Rs is the volume coefficient of the particles, cp is the fluctuating velocity given by 〈cp′2〉 ) (κkp)/(mp), κ is the Boltzmann coefficients (1.3806504 × 10-23 J K-1), mp is the mass of particle (kg), kp is the instantaneous kinetic energy of particles, and e is the collision coefficient of restitution (e ) 1.0). According to the k-ε-Ap model, discrete phase turbulent fluctuation can be attributed to the continuous phase, thus kp ) [1 + (τs)/(τt)]-1 · kl. τs is the particle dynamic response time (τs ) (Fsds2)/(18 µ)), τt is the pulsation of the continuous phase (τt ) (2)/(3)(Cµ3/4kl)/(εl)), Fs is the particle density (kg/m3), ds is the diameter of the particle (m), µ is the liquid viscosity (Pa · s); kl is the turbulent energy (N · m), and εl is the diffusivity of kl (N/s). The last term, Fx, includes other forces such as the virtual mass force, the pressure gradient force, and the lift force. Fp is the pressure force given by Fp ) -Vd∇p, where Vd is the particle volume and ∇p is the gradient in the carrier fluid; p includes any hydrostatic components. Fam is the so-called “virtual, mass” force, that is, that required to accelerate the carrier fluid “entrained” by the droplet. The expression for this is Fam ) -CamFVd(d(Us - Ul))/(dt), where Cam is the virtual mass coefficient, usually set to 0.5. Fl is the lift force given by Fl ) CLRsFl(ur) × (∇ × ul), where Cl is the lift coefficient, usually set to 0.5, Rs is the volume fraction of particles, ul is the flow velocity (m/s), and ur is the relative velocity between the two phases (m/s). Ul is the instantaneous velocity in the x-direction in Cartesian coordinates, ul is the mean velocity, and u′ is the fluctuating velocity. Ul ) ul + u'
(7)
The random-walk technique was used to model fluctuations in the turbulence of the flow.20 The turbulence was modeled by eddies defined by the Gaussian-distributed random fluctuations in the u′, V′, and w′ velocity.
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u' ) V' ) w' ) ζ
2k3
(8)
According to the hypothesis of isotropic turbulence, ζ is a normally distributed random number that represents the three directions, and k is the kinetic energy of turbulence (N m). In turbulent flows, a random-walk model is employed to model turbulent fluctuations of the flow, and the trajectories of particles are modeled through the continuum flow approach. The particle trajectory equation was solved by integrating the equation over regular time intervals. The particle velocity, us, was obtained by solving the particle force equation, and the particle trajectory was obtained by substituting the particle force equation into eq 9. dxi ) usi dt
(9)
With this method, the trajectories of the particles could be calculated, and particle behavior in the flow field and the removal efficiency could be determined. 2.2. Boundary Conditions. The boundary conditions for the liquid described in ref 6 were applied to this study. We choose “rebound” as the wall boundary condition for the particles. Rebound means that the impinging particle bounces off the wall after the impact. Both the tangential velocity and the normal velocity are partly lost. en and et are defined as the normal and tangential restitution coefficients, respectively. The former depends on the particle incidence angle θ (measured from the wall) as en ) 0.993 - 1.76θ + 1.56θ2 - 0.49θ3, while the latter is constant et ) (5)/(7).
of the experimental setup is shown in the right-hand side of Figure 1. Because of the difficulties associated with sludge disposal, the sediment in the wastewater was separated according to particle size by controlling the hydraulic load and stability of the flow. A schematic depiction of the process is shown in Figure 1b. To separate the particles by size, a sedimentation tank was divided into two stages by an inserting plate. In both stages, coarse particles settle to the bottom of the tank and are quickly dewatered. Alternatively, fine particles are removed by flocculation and sedimentation, predewatered in thickener, and dewatered by vacuum dehydration. The HRT of the two-stage sedimentation tanks was varied by regulating the inflow discharge rate. To measure the dewatering performance of the tank, the sludge resistance of the resulting sediment was determined according to the following procedure: (1) 80 mL of effluent was collected from each stage of the two-stage sedimentation tank and was filtered through an ultrafiltration cup with a FB-01T solvent filter and a 12.56 cm2 microporous membrane. (2) The water samples were filtered for 2 min until filtrate was no longer obtained from the sample. (3) The samples were vacuum pumped at 4.9 × 104 Pa, and the volume of the filtrate, V, was recorded every 15 s until the vacuum could no longer be maintained. (4) The filter cake was dried and weighed, and a curve with a slope equal to b, an abscissa of V, and an ordinate of t/V was plotted. The sludge resistance R of the two-stage sediment was obtained by substituting the value of b into the Carman filtration equation, which can be expressed as
3. Experimental Section As shown in Figure 1a, the experiments were conducted in a hydropower station in southeast China, and a 3D CAD drawing
Figure 1. Model and technological process: (a) experimental model, and (b) technological process.
R)
2PA2 × b µ×c
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Figure 2. Sludge resistance and removal efficiency: (a) sludge resistance of first-stage sediment, and (b) sludge resistance of second-stage sediment.
4. Computational Mesh and Boundary Conditions
Figure 3. The total removal efficiency.
where Ri s the sludge resistance (cm g-1), P is vacuum (Pa), A is filtration area (cm2), B is straight slope, µ is viscosity (Pa s-1), and C is mass of the filter cake per unit volume of filtrate (g mL-1). In each experiment, 100 mL of the original water was tested, and the effluent from the first-stage and second-stage sedimentation tank was collected and filtered through leaching bottles. The residue that remained on the filter paper was dried to a constant weight. The total removal efficiency was calculated and is shown in Figure 3. According to the results shown in Figures 2 and 3, the removal efficiency and resistance of the sludge from the firststage sediment were relatively low at an HRT of 4/12 min, 5/10 min, and 7/21 min. At an HRT of 15/30 and 20/40 min, the resistance of the sludge was high, which can lead to dewatering difficulties. Moreover, the sludge resistance at an HRT of 10/ 30 min was greater than the resistance of the sludge obtained at an HRT of 12/24 min; thus, an HRT of 12/24 min was applied to the theoretical studies.
4.1. Mesh and Boundary Conditions. The models were validated by performing a pilot test in a rectangular basin with a length and width of 3 and 2.5 m, respectively. The basin was equipped with two baffles (0.3 m in length) and an inserting plate, which was used to divide the tank into two sections with different HRTs. Physical models with HRTs of 4/12 min, 7/21 min, 10/30 min are shown in Figure 4a, and physical models of the remaining conditions are shown in Figure 4b. Figure 5 shows the computational meshes used in each experiment. 4.2. Mesh Sensitivity Test. A grid dependency study was performed to eliminate errors due to the coarseness of the grid and also to optimize the accuracy, numerical stability, convergence, and computational time of the simulation. The selected grid was comprised of 8060 quadrilateral elements; however, two other grids (one with 15 840 elements, and one with 2348 elements) were also used to determine the effect of grid resolution. The independence of the grid was verified by comparing the computed velocity and particle trajectory of three different mesh densities (2348, 8060, and 15 840), as shown in Figure 6. Figure 7 shows the velocity distribution obtained at a mesh number of 2348, 8060, and 15 840. The numerical removal efficiency of the two-state sedimentation tank at a mesh density of 2348, 8060, and 15 840 was 50%, 57.5%, and 66.4%, and the relative error was 58%, 7.52%, and 6.80%, respectively. Alternatively, the experimental removal efficiency was 62.17% at an HRT of 12/24 min. These results suggested that the velocity distribution remained satisfactory as the mesh density increased; however, the consumption of resources increased significantly. Moreover, the solutions obtained from the grid containing 8060 elements, which provided reasonable accuracy and computational efficiency, were considered to be independent
Figure 4. Sketch of the sedimentation tank with different HRTs (unit: mm): (a) 4/12 min HRT, and (b) 12/24 min HRT.
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Figure 5. Computational mesh of the sedimentation tank: (a) computational mesh of the 4/12 min HRT, and (b) computational mesh of the 12/24 min HRT.
5. Results and Discussion
Figure 6. Computational grids for the sedimentation tank: (a) 2348 elements, (b) 8060 elements, and (c) 15 840 elements.
of the grid mesh. Thus, the time step of the sedimentation tank was optimized at a mesh density of 8060. Figure 8 shows the particle trajectories at a time step of 0.01, 0.05, and 0.5 s. As the time interval decreased, particle trajectories remained reasonable, but the consumption of resources increased sharply. At a time interval of 0.01, 0.05, and 0.5 s, the computing time was 10, 5, and 3 h. Thus, a time step of 0.05 s, which provided reasonable accuracy and computational efficiency, was selected for the studies.
5.1. Numerical Simulation of the Water Field. To understand particle behavior, recirculation zones in the flow field were identified because these features have a significant impact on the settling of sand. Because of the presence of the inserting plate, sludge hoppers, first-stage baffle, and second-stage baffle, the flow pattern displays the characteristics of both the upper influent and the lower effluent, and short flow was not observed in the sedimentation tank. Figure 7b shows the simulated velocity field of water. As shown in the figure, the inlet jet sinks to the sludge hopper and develops into an underflow due to the presence of the first-stage baffle. Moreover, a small recirculation region was observed beneath the inlet due to the effect of the first-stage baffle and the sludge hopper. Two other recirculation regions appeared behind the first-stage baffle and the second-stage baffle, respectively. These recirculation regions may decrease the effective volume of the sedimentation tank and influence particle settling. As the distance from the second-stage baffle increased, the velocity of particles in most regions (x ) 1.75-3 m) of the second-stage sedimentation tank becomes relatively homogeneous and slow. The experimental device classification was implemented by the inserting plate. Figure 9 shows the velocity field corresponding to an HRT of 4/12 min condition, which was similar to that of the 12/24 min condition, and there is no need for further discussion. Figure 10 shows a contour plot of the velocity in the tank. The current in the center of the tank flowed directly to the sidewalls from the center plane (z ) 0.1365 m), and the velocity was axisymmetric. Remarkable changes in the velocity were observed near the inserting plate and the outlet due to the effect of the inserting plate, sludge hopper, and effluent wire.
Figure 7. Distribution of the velocity for different mesh densities (unit: m/s): (a) 2348 elements, (b) 8060 elements, and (c) 15 840 elements.
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Figure 8. Distribution of particle trajectories for different time steps: (a) 0.01 s, (b) 0.05 s, and (c) 0.5 s.
Figure 9. Velocity field of water in a two-state sedimentation tank (4/12 min HRT, unit: m/s).
Figure 10. Contour plot of the velocity in the sedimentation tank (unit: m/s).
The distribution of velocities at different heights and a constant z of 0.1365 m was provided in Figure 12, where y ) 0.264 m, 0.132 m, and 0.066 m denote the near-surface region, middle region, and near-bottom region, respectively. Obvious changes in the velocity were observed at different heights. According to the results shown in Figure 11a, the u velocity at the bottom of the tank (y ) 0.066 m) was negative at x ) 0-0.2 m, 0.55-0.7 m, and 1.3-1.8 m, which suggested that three recirculation zones were present due to the effects of the sludge hoppers and first-stage and second-stage baffles. Moreover, the results indicated that the u velocity at the surface of the tank (y ) 0.264 m) reached a maximum at x ) 0.02 m (near the inlet) and decreased as the distance from the inlet increased. However, the u velocity increased near the inserting plate at x ) 0.75 m. The distribution of the u velocity in the middle of the tank (y ) 0.132 m) was relatively flat, and areas with negative values were relatively small, which suggested that the recirculation zones in the middle of the tank were also small. As shown in Figure 11b, significant changes in the V velocity were observed at the bottom of the tank (y ) 0.066 m). In addition, periodic peaks and valleys in the V velocity were observed due to the effects of the inserting plate and the baffles.
The first-stage and second-stage baffles cause the flow to move downward, reducing the V velocities to -0.20 × 10-2 and -0.010 m/s, respectively. The V velocity in the middle of the tank was similar to the V velocity at the bottom of the tank. Alternatively, at the surface of the tank (y ) 0.264 m), a significant upward current was observed, and the V velocity reached a maximum value of 0.82 × 10-3 m/s near the inserting plate (x ) 0.75 m). According to the results shown in Figure 11c, the w velocity was not uniform throughout the tank and was 1 order of magnitude less than the u and V velocities. Because the w velocity varied significantly along the width of the tank and its distribution was similar behind the firststage and second-stage baffles (see Figure 12), the following discussion is focused primarily on the w velocity behind the first-stage baffle (x ) 0.3-1.0 m). Figure 12 shows the distribution of the w velocity at different heights. As shown in the figure, at z ) 0-0.125 m and x ) 0.3-0.5 m, the w velocity was negative, which indicated that the area of the recirculation zone increased with an increase in height. At y ) 0.066 m, z ) 0.15-0.25 m, x ) 0.5-0.7 m, and y ) 0.132 m, z ) 0.15-0.25 m, x ) 0.5-0.7 m, the w velocity increased sharply and reached a maximum value of 0.50 × 10-3
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Figure 11. Distribution of the velocity components at z ) 0.1365 m: (a) u velocity, (b) V velocity, and (c) w velocity.
Figure 12. Distribution of the w velocity at different heights (unit: m/s): (a) y ) 0.066 m, (b) y ) 0.132 m, and (c) y ) 0.264 m.
m/s, indicating that the velocity of the sludge rapidly increased as the flow of water rushed upward from the sludge hoppers. At y ) 0.264 m, z ) 0.15-0.25 m, x ) 0.7-0.75 m, the w velocity increased to 1.0 × 10-3 m/s due to the proximity of the inserting plate, which narrowed the flow section and increased the w velocity. 5.2. The Proportion of Sandstone in the First-Stage Effluent. The particulate matter in the first-stage effluent was sorted by molecular sieves with a mesh of 160, 300, 800, and 1600 (100, 50, 20, and 10 µm, respectively). After the residue was washed, dried, and weighed, the particle size distribution of the sandstone was calculated and is shown in Figure 13a. As shown in Figure 13b, the numerical results were in good agreement with the experimental data. Thus, the model can reasonably
simulate the water flow field and trajectories of parcels in the sedimentation tank. The experimental data indicated that larger particles display a greater removal efficiency than smaller particles. Figure 14 shows the settling performance of different sized particles. According to the particle trajectories shown in Figure 14, the particle size had a significant effect on the removal efficiency. Before the first-stage baffle, second-stage baffle, and the inserting plate, the velocity of the flow was high and the rolling action of the particles was apparent. Particles larger than 50 µm displayed a satisfactory settling performance, and the majority of these particles rapidly settled to the sludge hoppers (see Figure 14a). However, the effect of water on particles between 10 and 50 µm was diverse. For instance, a fraction of
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Figure 15. The effect of collision force on particle load: (a) without collision force, and (b) with collision force.
Figure 16. Particle trajectories under steady-state conditions.
Figure 13. Numerical results and experimental results of the particle size distribution of sandstone in the first-stage effluent: (a) experimental sandstone data, and (b) the numerical and experimental results of the particle size distribution of sandstone.
Figure 14. Trajectories of different size particles: (a) >50 µm, (b) 10-50 µm, and (c)
