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Type 316Ti(UNS 31635) is a Titanium stabilized austenitic chromium-nickel stainless steel containing molybdenum. This addition increases corrosion resistance, improves resistance to pitting chloride ion solutions and provide increased strength at elevated temperatures. Properties are similar to those of type 316 except that 316Ti due to its Titanium addition can be used at elevated sensitisation temperatures. Corrosion resistance is improved, particularly against sulfuric, hydrochloric, acetic, formic and tartaric acids, acid sulfates and alkaline chlorides.
Chemical composition:
|
C |
Si |
Mn |
P |
S |
Cr |
Ni |
Mo |
|
≤ 0.08 |
≤ 1.0 |
≤ 2.0 |
≤ 0.045 |
≤ 0.03 |
16.0 - 18.0 |
10.0 - 14.0 |
2.0 - 3.0 |
Properties: Annealed：
Ultimate Tensile Strength: 75 KSI min (515 MPa min)
Yield Strength: (0.2% Offset) 30 KSI min (205 MPa min)
Elongation: 40% min
Hardness: Rb 95 max
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In this study, the hydrodynamics of flocculation is evaluated by experimental and numerical investigation of the turbulent flow velocity field in a laboratory scale paddle flocculator. The turbulent flow that promotes particle aggregation or floc breakup is complex and is considered and compared in this paper using two turbulence models, namely SST k-ω and IDDES. The results show that IDDES provides a very small improvement over SST k-ω, which is sufficient to accurately simulate flow within a paddle flocculator. The fit score is used to investigate the convergence of PIV and CFD results, and to compare the results of the CFD turbulence model used. The study also focuses on quantifying the slip factor k, which is 0.18 at low speeds of 3 and 4 rpm compared to the usual typical value of 0.25. Decreasing k from 0.25 to 0.18 increases the power delivered to the fluid by about 27-30% and increases the velocity gradient (G) by about 14%. This means that more agitation is provided than expected, therefore less energy is consumed and therefore the energy consumption in the flocculation unit of the drinking water treatment plant can be lower.
In water purification, the addition of coagulants destabilizes small colloidal particles and impurities, which then combine to form flocculation at the flocculation stage. Flakes are loosely bound fractal aggregates of mass, which are then removed by settling. Particle properties and liquid mixing conditions determine the efficiency of the flocculation and treatment process. Flocculation requires slow agitation for a relatively short period of time and a lot of energy to agitate large volumes of water1.
During flocculation, the hydrodynamics of the entire system and the chemistry of coagulant-particle interaction determine the rate at which a stationary particle size distribution is achieved2. When particles collide, they stick to each other3. Oyegbile, Ay4 reported that collisions depend on the flocculation transport mechanisms of Brownian diffusion, fluid shear and differential settling. When the flakes collide, they grow and reach a certain size limit, which can lead to breakage, since the flakes cannot withstand the force of hydrodynamic forces5. Some of these broken flakes recombine into smaller ones or the same size6. However, strong flakes can resist this force and maintain their size and even grow7. Yukselen and Gregory8 reported on studies related to the destruction of flakes and their ability to regenerate, showing that irreversibility is limited. Bridgeman, Jefferson9 used CFD to estimate the local influence of mean flow and turbulence on floc formation and fragmentation through local velocity gradients. In tanks equipped with rotor blades, it is necessary to vary the speed at which the aggregates collide with other particles when they are sufficiently destabilized in the coagulation phase. By using CFD and lower rotation speeds of around 15 rpm, Vadasarukkai and Gagnon11 were able to achieve the G value for conical paddle flocculation, thereby minimizing power consumption for agitation. However, operation at higher G values may lead to flocculation. They investigated the effect of mixing speed on determining the average velocity gradient of a pilot paddle flocculator. They rotate at a speed of more than 5 rpm.
Korpijärvi, Ahlstedt12 used four different turbulence models to study the flow field on a tank test bench. They measured the flow field with a laser Doppler anemometer and PIV and compared the calculated results with the measured results. de Oliveira and Donadel13 have proposed an alternative method for estimating velocity gradients from hydrodynamic properties using CFD. The proposed method was tested on six flocculation units based on helical geometry. assessed the effect of retention time on flocculants and proposed a flocculation model that can be used as a tool to support rational cell design with low retention times14. Zhan, You15 proposed a combined CFD and population balance model to simulate flow characteristics and floc behavior in full scale flocculation. Llano-Serna, Coral-Portillo16 investigated the flow characteristics of a Cox-type hydroflocculator in a water treatment plant in Viterbo, Colombia. Although CFD has its advantages, there are also limitations such as numerical errors in calculations. Therefore, any numerical results obtained should be carefully examined and analyzed in order to draw critical conclusions17. There are few studies in the literature on the design of horizontal baffle flocculators, while recommendations for the design of hydrodynamic flocculators are limited18. Chen, Liao19 used an experimental setup based on the scattering of polarized light to measure the state of polarization of scattered light from individual particles. Feng, Zhang20 used Ansys-Fluent to simulate the distribution of eddy currents and swirl in the flow field of a coagulated plate flocculator and an inter-corrugated flocculator. After simulating turbulent fluid flow in a flocculator using Ansys-Fluent, Gavi21 used the results to design the flocculator. Vaneli and Teixeira22 reported that the relationship between the fluid dynamics of spiral tube flocculators and the flocculation process is still poorly understood to support a rational design. de Oliveira and Costa Teixeira23 studied the efficiency and demonstrated the hydrodynamic properties of the spiral tube flocculator through physics experiments and CFD simulations. Many researchers have studied coiled tube reactors or coiled tube flocculators. However, detailed hydrodynamic information on the response of these reactors to various designs and operating conditions is still lacking (Sartori, Oliveira24; Oliveira, Teixeira25). Oliveira and Teixeira26 present original results from theoretical, experimental and CFD simulations of a spiral flocculator. Oliveira and Teixeira27 proposed to use a spiral coil as a coagulation-flocculation reactor in combination with a conventional decanter system. They report that the results obtained for turbidity removal efficiency are significantly different from those obtained with commonly used models for evaluating flocculation, suggesting caution when using such models. Moruzzi and de Oliveira [28] modeled the behavior of a system of continuous flocculation chambers under various operating conditions, including variations in the number of chambers used and the use of fixed or scaled cell velocity gradients. Romphophak, Le Men29 PIV measurements of instantaneous velocities in quasi-two-dimensional jet cleaners. They found strong jet-induced circulation in the flocculation zone and estimated local and instantaneous shear rates.
Shah, Joshi30 report that CFD offers an interesting alternative for improving designs and obtaining virtual flow characteristics. This helps to avoid extensive experimental setups. CFD is increasingly being used to analyze water and wastewater treatment plants (Melo, Freire31; Alalm, Nasr32; Bridgeman, Jefferson9; Samaras, Zouboulis33; Wang, Wu34; Zhang, Tejada-Martínez35). Several investigators have performed experiments on can test equipment (Bridgeman, Jefferson36; Bridgeman, Jefferson5; Jarvis, Jefferson6; Wang, Wu34) and perforated disc flocculators31. Others have used CFD to evaluate hydroflocculators (Bridgeman, Jefferson5; Vadasarukkai, Gagnon37). Ghawi21 reported that mechanical flocculators require regular maintenance as they often break down and require a lot of electricity.
The performance of a paddle flocculator is highly dependent on the hydrodynamics of the reservoir. The lack of quantitative understanding of the flow velocity fields in such flocculators is clearly noted in the literature (Howe, Hand38; Hendricks39). The entire water mass is subject to the movement of the flocculator impeller, so slippage is expected. Typically, the fluid velocity is less than the blade velocity by the slip factor k, which is defined as the ratio of the velocity of the body of water to the velocity of the paddle wheel. Bhole40 reported that there are three unknown factors to consider when designing a flocculator, namely the velocity gradient, the drag coefficient, and the relative velocity of the water relative to the blade.
Camp41 reports that when considering high speed machines, the speed is about 24% of the rotor speed and as high as 32% for low speed machines. In the absence of septa, Droste and Ger42 used a k value of 0.25, while in the case of septa, k ranged from 0 to 0.15. Howe, Hand38 suggest that k is in the range of 0.2 to 0.3. Hendrix39 related the slip factor to rotational speed using an empirical formula and concluded that the slip factor was also within the range established by Camp41. Bratby43 reported that k is about 0.2 for impeller speeds from 1.8 to 5.4 rpm and increases to 0.35 for impeller speeds from 0.9 to 3 rpm. Other researchers report a wide range of drag coefficient (Cd) values from 1.0 to 1.8 and slip coefficient k values from 0.25 to 0.40 (Feir and Geyer44; Hyde and Ludwig45; Harris, Kaufman46; van Duuren47; and Bratby and Marais48). The literature does not show significant progress in defining and quantifying k since Camp41′s work.
The flocculation process is based on turbulence to facilitate collisions, where the velocity gradient (G) is used to measure turbulence/flocculation. Mixing is the process of quickly and evenly dispersing chemicals in water. The degree of mixing is measured by the velocity gradient:
where G = velocity gradient (sec-1), P = power input (W), V = volume of water (m3), μ = dynamic viscosity (Pa s).
The higher the G value, the more mixed. Thorough mixing is essential to ensure uniform coagulation. The literature indicates that the most important design parameters are mixing time (t) and velocity gradient (G). The flocculation process is based on turbulence to facilitate collisions, where the velocity gradient (G) is used to measure turbulence/flocculation. Typical design values for G are 20 to 70 s–1, t is 15 to 30 minutes, and Gt (dimensionless) is 104 to 105. Fast mix tanks work best with G values of 700 to 1000, with time stay about 2 minutes.
where P is the power imparted to the liquid by each flocculator blade, N is the rotation speed, b is the blade length, ρ is the water density, r is the radius, and k is the slip coefficient. This equation is applied to each blade individually and the results are summed to give the total power input of the flocculator. A careful study of this equation shows the importance of the slip factor k in the design process of a paddle flocculator. The literature does not state the exact value of k, but instead recommends a range as previously stated. However, the relationship between the power P and the slip coefficient k is cubic. Thus, provided that all parameters are the same, for example, changing k from 0.25 to 0.3 will lead to a decrease in the power transmitted to the fluid per blade by about 20%, and reducing k from 0.25 to 0.18 will increase her. by about 27-30% per vane The power imparted to the fluid. Ultimately, the effect of k on sustainable paddle flocculator design needs to be investigated through technical quantification.
Accurate empirical quantification of slippage requires flow visualization and simulation. Therefore, it is important to describe the tangential speed of the blade in water at a certain rotational speed at different radial distances from the shaft and at different depths from the water surface in order to evaluate the effect of different blade positions.
In this study, the hydrodynamics of flocculation is evaluated by experimental and numerical investigation of the turbulent flow velocity field in a laboratory scale paddle flocculator. The PIV measurements are recorded on the flocculator, creating time-averaged velocity contours showing the velocity of water particles around the leaves. In addition, ANSYS-Fluent CFD was used to simulate the swirling flow inside the flocculator and create time-averaged velocity contours. The resulting CFD model was confirmed by evaluating the correspondence between the PIV and CFD results. The focus of this work is on quantifying the slip coefficient k, which is a dimensionless design parameter of a paddle flocculator. The work presented here provides a new basis for quantifying the slip coefficient k at low speeds of 3 rpm and 4 rpm. The implications of the results directly contribute to a better understanding of the hydrodynamics of the flocculation tank.
The laboratory flocculator consists of an open-top rectangular box with an overall height of 147 cm, a height of 39 cm, an overall width of 118 cm, and an overall length of 138 cm (Fig. 1). The main design criteria developed by Camp49 were used to design a laboratory scale paddle flocculator and apply the principles of dimensional analysis. The experimental facility was built at the Environmental Engineering Laboratory of the Lebanese American University (Byblos, Lebanon).
The horizontal axis is located at a height of 60 cm from the bottom and accommodates two paddle wheels. Each paddle wheel consists of 4 paddles with 3 paddles on each paddle for a total of 12 paddles. Flocculation requires gentle agitation at a low speed of 2 to 6 rpm. The most common mixing speeds in flocculators are 3 rpm and 4 rpm. The laboratory scale flocculator flow is designed to represent the flow in the flocculation tank compartment of a drinking water treatment plant. Power is calculated using the traditional equation 42 . For both rotation speeds, the speed gradient \(\stackrel{\mathrm{-}}{\text{G}}\) is greater than 10 \({\text{sec}}^{-{1}}\) , the Reynolds number indicates turbulent flow (Table 1).
PIV is used to achieve accurate and quantitative measurements of fluid velocity vectors simultaneously at a very large number of points50. The experimental setup included a lab-scale paddle flocculator, a LaVision PIV system (2017), and an Arduino external laser sensor trigger. To create time-averaged velocity profiles, PIV images were recorded sequentially at the same location. The PIV system is calibrated such that the target area is at the midpoint of the length of each of the three blades of a particular paddle arm. The external trigger consists of a laser located on one side of the flocculator width and a sensor receiver on the other side. Each time the flocculator arm blocks the laser path, a signal is sent to the PIV system to capture an image with the PIV laser and camera synchronized with a programmable timing unit. On fig. 2 shows the installation of the PIV system and the image acquisition process.
The recording of PIV was started after the flocculator was operated for 5–10 min to normalize the flow and take into account the same refractive index field. Calibration is achieved by using a calibration plate immersed in the flocculator and placed at the midpoint of the length of the blade of interest. Adjust the position of the PIV laser to form a flat light sheet directly above the calibration plate. Record the measured values for each rotation speed of each blade, and the rotation speeds chosen for the experiment are 3 rpm and 4 rpm.
For all PIV recordings, the time interval between two laser pulses was set in the range from 6900 to 7700 µs, which allowed a minimum particle displacement of 5 pixels. Pilot tests were carried out on the number of images required to obtain accurate time-averaged measurements. Vector statistics were compared for samples containing 40, 50, 60, 80, 100, 120, 160, 200, 240, and 280 images. A sample size of 240 images was found to give stable time-averaged results given that each image consists of two frames.
Since the flow in the flocculator is turbulent, a small interrogation window and a large number of particles are required to resolve small turbulent structures. Several iterations of size reduction are applied along with a cross-correlation algorithm to ensure accuracy. An initial polling window size of 48×48 pixels with 50% overlap and one adaptation process was followed by a final polling window size of 32×32 pixels with 100% overlap and two adaptation processes. In addition, glass hollow spheres were used as seed particles in the flow, which allowed at least 10 particles per polling window. The PIV recording is initiated by a trigger source within a Programmable Timing Unit (PTU), which is responsible for operating and synchronizing the laser source and the camera.
The commercial CFD package ANSYS Fluent v 19.1 was used to develop the 3D model and solve the basic flow equations.
Using ANSYS-Fluent, a 3D model of a laboratory-scale paddle flocculator was created. The model is made in the form of a rectangular box, consisting of two paddle wheels mounted on a horizontal axis, like the laboratory model. The model without freeboard is 108 cm high, 118 cm wide and 138 cm long. A horizontal cylindrical plane has been added around the mixer. Cylindrical plane generation should implement the rotation of the entire mixer during the installation phase and simulate the rotating flow field inside the flocculator, as shown in Fig. 3a.
3D ANSYS-fluent and model geometry diagram, ANSYS-fluent flocculator body mesh on the plane of interest, ANSYS-fluent diagram on the plane of interest.
The model geometry consists of two regions, each of which is a fluid. This is achieved using the logical subtraction function. First subtract the cylinder (including mixer) from the box to represent the liquid. Then subtract the mixer from the cylinder, resulting in two objects: the mixer and the liquid. Finally, a sliding interface was applied between the two areas: a cylinder-cylinder interface and a cylinder-mixer interface (Fig. 3a).
The meshing of the constructed models has been completed to meet the requirements of the turbulence models that will be used to run the numerical simulations. An unstructured mesh with expanded layers near the solid surface was used. Create expansion layers for all walls with a growth rate of 1.2 to ensure that complex flow patterns are captured, with a first layer thickness of \(7\mathrm{ x }{10}^{-4}\) m to ensure that \ ( {\text {y))^{+}\le 1.0\). The body size is adjusted using the tetrahedron fitting method. A front side size of two interfaces with an element size of 2.5 × \({10}^{-3}\) m is created, and a mixer front size of 9 × \({10}^{-3}\ ) m is applied. The initial generated mesh consisted of 2144409 elements (Fig. 3b).
A two-parameter k–ε turbulence model was chosen as the initial base model. To accurately simulate the swirling flow inside the flocculator, a more computationally expensive model was chosen. The turbulent swirling flow inside the flocculator was numerically investigated using two CFD models: SST k–ω51 and IDDES52. The results of both models were compared with experimental PIV results to validate the models. First, the SST k-ω turbulence model is a two-equation turbulent viscosity model for fluid dynamics applications. This is a hybrid model combining the Wilcox k-ω and k-ε models. The mixing function activates the Wilcox model near the wall and the k-ε model in the oncoming flow. This ensures that the correct model is used throughout the flow field. It accurately predicts flow separation due to adverse pressure gradients. Secondly, the Advanced Deferred Eddy Simulation (IDDES) method, widely used in the Individual Eddy Simulation (DES) model with the SST k-ω RANS (Reynolds-Averaged Navier-Stokes) model, was selected. IDDES is a hybrid RANS-LES (large eddy simulation) model that provides a more flexible and user-friendly resolution scaling (SRS) simulation model. It is based on the LES model to resolve large eddies and reverts to SST k-ω to simulate small scale eddies. Statistical analyzes of the results from the SST k–ω and IDDES simulations were compared with the PIV results to validate the model.
A two-parameter k–ε turbulence model was chosen as the initial base model. To accurately simulate the swirling flow inside the flocculator, a more computationally expensive model was chosen. The turbulent swirling flow inside the flocculator was numerically investigated using two CFD models: SST k–ω51 and IDDES52. The results of both models were compared with experimental PIV results to validate the models. First, the SST k-ω turbulence model is a two-equation turbulent viscosity model for fluid dynamics applications. This is a hybrid model combining the Wilcox k-ω and k-ε models. The mixing function activates the Wilcox model near the wall and the k-ε model in the oncoming flow. This ensures that the correct model is used throughout the flow field. It accurately predicts flow separation due to adverse pressure gradients. Secondly, the Advanced Deferred Eddy Simulation (IDDES) method, widely used in the Individual Eddy Simulation (DES) model with the SST k-ω RANS (Reynolds-Averaged Navier-Stokes) model, was selected. IDDES is a hybrid RANS-LES (large eddy simulation) model that provides a more flexible and user-friendly resolution scaling (SRS) simulation model. It is based on the LES model to resolve large eddies and reverts to SST k-ω to simulate small scale eddies. Statistical analyzes of the results from the SST k–ω and IDDES simulations were compared with the PIV results to validate the model.
Use a pressure-based transient solver and use gravity in the Y direction. Rotation is achieved by assigning a mesh motion to the mixer, where the origin of the rotation axis is at the center of the horizontal axis and the direction of the rotation axis is in the Z direction. A mesh interface is created for both model geometry interfaces, resulting in two bounding box edges. As in the experimental technique, the rotation speed corresponds to 3 and 4 revolutions.
The boundary conditions for the walls of the mixer and the flocculator were set by the wall, and the top opening of the flocculator was set by the outlet with zero gauge pressure (Fig. 3c). SIMPLE pressure-velocity communication scheme, discretization of the gradient space of second-order functions with all parameters based on least squares elements. The convergence criterion for all flow variables is the scaled residual 1 x \({10}^{-3}\). The maximum number of iterations per time step is 20, and the time step size corresponds to a rotation of 0.5°. The solution converges at the 8th iteration for the SST k–ω model and at the 12th iteration using IDDES. In addition, the number of time steps was calculated so that the mixer made at least 12 revolutions. Apply data sampling for time statistics after 3 rotations, which allows normalization of the flow, similar to the experimental procedure. Comparing the output of the speed loops for each revolution gives exactly the same results for the last four revolutions, indicating that a steady state has been reached. The extra revs didn’t improve the medium speed contours.
The time step is defined in relation to the rotation speed, 3 rpm or 4 rpm. The time step is refined to the time required to rotate the mixer by 0.5°. This turns out to be sufficient, since the solution converges easily, as described in the previous section. Thus, all numerical calculations for both turbulence models were carried out using a modified time step of 0.02 \(\stackrel{\mathrm{-}}{7}\) for 3 rpm, 0.0208 \(\stackrel{ \mathrm{-} {3}\) 4 rpm. For a given refinement time step, the Courant number of a cell is always less than 1.0.
To explore model-mesh dependence, results were first obtained using the original 2.14M mesh and then the refined 2.88M mesh. Grid refinement is achieved by reducing the cell size of the mixer body from 9 × \({10}^{-3}\) m to 7 × \({10}^{-3}\) m. For the original and refined meshes of the two models turbulence, the average values of the velocity modules in different places around the blade were compared. The percentage difference between the results is 1.73% for the SST k–ω model and 3.51% for the IDDES model. IDDES shows a higher percentage difference because it is a hybrid RANS-LES model. These differences were considered insignificant, so the simulation was performed using the original mesh with 2.14 million elements and a rotation time step of 0.5°.
The reproducibility of the experimental results was examined by performing each of the six experiments a second time and comparing the results. Compare the speed values at the center of the blade in two series of experiments. The average percentage difference between the two experimental groups was 3.1%. The PIV system was also independently recalibrated for each experiment. Compare the analytically calculated speed at the center of each blade with the PIV speed at the same location. This comparison shows the difference with a maximum percentage error of 6.5% for blade 1.
Before quantifying the slip factor, it is necessary to scientifically understand the concept of slip in a paddle flocculator, which requires studying the flow structure around the paddles of the flocculator. Conceptually, the slip coefficient is built into the design of paddle flocculators to take into account the speed of the blades relative to the water. The literature recommends that this speed be 75% of the blade speed, so most designs typically use a k of 0.25 to account for this adjustment. This requires the use of velocity streamlines derived from PIV experiments to fully understand the flow velocity field and study this slip. Blade 1 is the innermost blade closest to the shaft, blade 3 is the outermost blade, and blade 2 is the middle blade.
The velocity streamlines on blade 1 show a direct rotating flow around the blade. These flow patterns emanate from a point on the right side of the blade, between the rotor and the blade. Looking at the area indicated by the red dotted box in Figure 4a, it is interesting to identify another aspect of the recirculation flow above and around the blade. Flow visualization shows little flow into the recirculation zone. This flow approaches from the right side of the blade at a height of about 6 cm from the end of the blade, possibly due to the influence of the first blade of the hand preceding the blade, which is visible in the image. Flow visualization at 4 rpm shows the same behavior and structure, apparently with higher speeds.
Velocity field and current graphs of three blades at two rotation speeds of 3 rpm and 4 rpm. The maximum average speed of the three blades at 3 rpm is 0.15 m/s, 0.20 m/s and 0.16 m/s respectively, and the maximum average speed at 4 rpm is 0.15 m/s, 0.22 m/s and 0.22 m/s, respectively. on three sheets.
Another form of helical flow was found between vanes 1 and 2. The vector field clearly shows that the water flow is moving upward from the bottom of vane 2, as indicated by the direction of the vector. As shown by the dotted box in Fig. 4b, these vectors do not go vertically upward from the blade surface, but turn to the right and gradually descend. On the surface of the blade 1, downward vectors are distinguished, which approach both blades and surround them from the recirculation flow formed between them. The same flow structure was determined at both rotation speeds with a higher speed amplitude of 4 rpm.
The velocity field of blade 3 does not make a significant contribution from the velocity vector of the previous blade joining the flow below blade 3. The main flow under blade 3 is due to the vertical velocity vector rising with the water.
The velocity vectors over the surface of the blade 3 can be divided into three groups, as shown in Fig. 4c. The first set is the set on the right edge of the blade. The flow structure in this position is straight to the right and up (i.e. towards blade 2). The second group is the middle of the blade. The velocity vector for this position is directed straight up, without any deviation and without rotation. The decrease in the velocity value was determined with an increase in the height above the end of the blade. For the third group, located on the left periphery of the blades, the flow is immediately directed to the left, i.e. to the wall of the flocculator. Most of the flow represented by the velocity vector goes up, and part of the flow goes horizontally down.
Two turbulence models, SST k–ω and IDDES, were used to construct time-averaged velocity profiles for 3 rpm and 4 rpm in the blade mean length plane. As shown in Figure 5, steady state is achieved by achieving absolute similarity between the velocity contours created by four successive rotations. In addition, the time-averaged velocity contours generated by IDDES are shown in Fig. 6a, while the time-averaged velocity profiles generated by SST k – ω are shown in Fig. 6a. 6b.
Using IDDES and time-averaged velocity loops generated by SST k–ω, IDDES has a higher proportion of velocity loops.
Carefully examine the speed profile created with IDDES at 3 rpm as shown in Figure 7. The mixer rotates clockwise and the flow is discussed according to the notes shown.
On fig. 7 it can be seen that on the surface of the blade 3 in the I quadrant there is a separation of the flow, since the flow is not constrained due to the presence of the upper hole. In quadrant II no separation of the flow is observed, since the flow is completely limited by the walls of the flocculator. In quadrant III, the water rotates at a much lower or lower speed than in the previous quadrants. The water in quadrants I and II is moved (ie rotated or pushed out) downward by the action of the mixer. And in quadrant III, the water is pushed out by the blades of the agitator. It is obvious that the water mass in this place resists the approaching flocculator sleeve. The swirling flow in this quadrant is completely separated. For quadrant IV, most of the airflow above vane 3 is directed towards the flocculator wall and gradually loses its size as the height increases to the top opening.
In addition, the central location includes complex flow patterns that dominate quadrants III and IV, as shown by the blue dotted ellipses. This marked area has nothing to do with the swirling flow in the paddle flocculator, as the swirling motion can be identified. This is in contrast to quadrants I and II where there is a clear separation between internal flow and full rotational flow.
As shown in fig. 6, comparing the results of IDDES and SST k-ω, the main difference between the velocity contours is the magnitude of the velocity immediately below blade 3. The SST k-ω model clearly shows that extended high-velocity flow is carried by blade 3 compared to IDDES.
Another difference can be found in quadrant III. From the IDDES, as mentioned earlier, rotational flow separation between the flocculator arms was noted. However, this position is strongly affected by the low velocity flow from the corners and the interior of the first blade. From SST k–ω for the same location, the contour lines show relatively higher velocities compared to IDDES because there is no confluent flow from other regions.
A qualitative understanding of the velocity vector fields and streamlines is required for a correct understanding of the flow behavior and structure. Given that each blade is 5 cm wide, seven velocity points were chosen across the width to provide a representative velocity profile. In addition, a quantitative understanding of the magnitude of velocity as a function of height above the blade surface is required by plotting the velocity profile directly over each blade surface and over a continuous distance of 2.5 cm vertically up to a height of 10 cm. See S1, S2 and S3 in the figure for more information. Appendix A. Figure 8 shows the similarity of the surface velocity distribution of each blade (Y = 0.0) obtained using PIV experiments and ANSYS-Fluent analysis using IDDES and SST k-ω. Both numerical models make it possible to accurately simulate the flow structure on the surface of the flocculator blades.
Velocity distributions PIV, IDDES and SST k–ω on the blade surface. The x-axis represents the width of each sheet in millimeters, with the origin (0 mm) representing the left periphery of the sheet and the end (50 mm) representing the right periphery of the sheet.
It is clearly seen that the speed distributions of the blades 2 and 3 are shown in Fig.8 and Fig.8. S2 and S3 in Appendix A show similar trends with height, while blade 1 changes independently. The velocity profiles of blades 2 and 3 become perfectly straight and have the same amplitude at a height of 10 cm from the end of the blade. This means that the flow becomes uniform at this point. This is clearly seen from the PIV results, which are well reproduced by IDDES. Meanwhile, the SST k–ω results show some differences, especially at 4 rpm.
It is important to note that blade 1 retains the same shape of the velocity profile in all positions and is not normalized in height, since the swirl formed in the center of the mixer contains the first blade of all arms. Also, compared to IDDES, PIV blade speed profiles 2 and 3 showed slightly higher speed values at most locations until they were nearly equal at 10 cm above the blade surface.
Post time: Feb-26-2023