Velocity field data were acquired for Taylor-Couette flow in the annulus gap between a rotating inner cylinder and a fixed concentric outer cylinder by particle image velocimetry. The flocculation efficiencies were also obtained in the same Taylor-Couette flow under the conditions corresponding to the velocity field measurement. It was shown that the flocculation efficiencies reach the maximum values due to the closed vortices in WVF and their contraction and expansion with time, but out of WVF range, the comparatively low flocculation efficiencies were obtained due to the no-closed vortices connected with each other.
Flocculation is a primary water treatment process that changes the size distribution of particles from a large number of small particles to a small number of large particles for removal in later processes. Particles increase in size because of collision with and attachment to other particles. These collisions can occur through the random Brownian motion of particles, fluid motion, and differential settling rate of particles. As far as the fluid motion is concerned, the work of Smoluchowski is the cornerstone of flocculation. According to Smoluchowski theory [
in which k is subscript denoting particle size, N is number concentration of the particles, t is time, r1 is the radius of primary particle, and G is the velocity gradient. In order to use Smoluchowski equation in turbulent flocculation condition, Camp and Stein developed the G-value as follows [
in which ε is the power input per unit mass, and ν is the kinematic viscosity. From that time, it has been widely accepted that the mixing conditions with the same G-value are almost identical from the flocculation point of view, and the G-value has been widely used in the design and scale-up of mixing process components. But since the middle of 1980s, some research results have been published that criticize and question the use of the G-value as a valid basis for the design of flocculation basins. For example, Oldsue [
It is well known that Taylor-Couette device is one of the traditional flocculation reactors [
where ω is the inner cylinder angular velocity, ri is the radius of the inner cylinder, d = r0 − ri is the annular gap width, and ν is the kinematic viscosity. The critical azimuthal Reynolds number at which Taylor instability occurs, Rec, depends upon the specific geometry of the flow device used(L. Wang et al. 2005; M. Soos et al. 2007). But it is convenient to define a reduced-Reynolds number ratio R(=Re/Rec) to parameterize the flow. L. Wang et al. found that the flow is approximately in the laminar vortex flow(TVF) regime when 1 < R ≤ 5.0, and in the wavy vortex flow(WVF) regime when 5.0 < R ≤ 20, and in the modulated wavy vortex flow(MWVF) regime when 20 < R ≤ 40, and in the turbulent vortex flow(TTVF) regime when R > 40 for their apparatus according to observation of the sequences of instantaneous velocity fields [
On the other hand, it is known that the particle image velocimetry (PIV) technique can measure the velocity of an entire flow field instantaneously to quantitatively reveal global structures of a complicated and unsteady flow [
By using the advanced technology of PIV and Taylor-Couette device, this study attempts to relate the flocculation efficiency to turbulent flow field, thus reveal some reasons which induce the turbulent flocculation and to give the better understanding of turbulent flocculation. It will be very helpful to researchers, designers and operators of flocculation in water treatment. To our knowledge, the relationships between the PIV data and flocculation efficiency presented here are the first reported.
The Taylor-Couette flow apparatus used in the present research was made in our laboratory. It consists of two concentric cylinders. The rotating inner cylinder is made of stainless steel, and has diameter 2ri = 75 mm. The fixed outer cylinder is made of Plexiglas, and has diameter 2ro = 100 mm. The resulting gap width is d = ro − ri = 12.5 mm, the radius ration is η = ro/ri = 0.75. The cylinder height L = 440 mm, the cylinder aspect ratio, Г = L/(r0 − ri) = 35.2. The inner cylinder is fitted with stainless steel drive shafts on the central axis. A ABB motor is used to drive the inner cylinder.
The FlowMap PIV system used in this study was bought from Dantec Dynamics of Danish. It consists of doubled pulsed Nd:YAG laser, high speed Flowsense 2M CCD camera, FlowMap system HUB, host computer and PIV software. The PIV software uses an adaptive-correlation technique to find the displacement of particles in a uniform grid before plotting the vectors using an interrogation region of 32 × 32 pixels with 50% overlap between adjacent interrogation regions. The PIV system was applied to the Taylor-Couette flow apparatus, as shown in
Optical distortions were eliminated by enclosing the outer cylinder in a square Plexiglas box and using a working fluid having a refractive index matched to that of Plexiglas. The flow was seeded with small tracer particles that reflect and scatter the laser light, and the CCD camera perpendicular to the laser sheet was used to capture the particle images in a plane illuminated by a laser light sheet. The FlowManager software was used to both Control the image acquisition, keep track of the recorded data, the set-ups and the experimental configuration. Data analysis is available in the FlowManager Analysis option. Besides functioning as a database, The FlowManager software also control the FlowMap system HUB through the run online menus. The maximum data collection rate for the system is 15 velocity vector fields per second. For each of reduced-Reynolds number ratio R studied, about 500 image pairs were captured. The time between laser pulses for an image pair vary with velocity fluid, Polyamide particles with an average diameter of 20 μm were used as seed particles at a concentration of 21.43 mg/L (10 particles within each interrogation area). The particles have a density of 1.03 × 103 kg/m3. The kinematic viscosity of the fluid was measured as 1.006 × 10−6 m2/s. To ensure that the flow state in the device was identical for each value of R studied, all experiments were performed using the following protocol. The rotation rate of the inner cylinder was maintained at any given angular velocity for at least 10 min, until the desired value of R was reached, and then the flow was expected to equilibrate for approximately 10 min before PIV data were collected.
2% suspension of kaolin was prepared as stock solutions. 1500 ml of tap water and 7.5 ml of above kaolin suspension were added to Taylor-Couette reactor. After the strong mixing by rotating of inner cylinder (500 rpm),
the turbidity of this water sample equals 100 NTU. 1%PAC solutions were added in different dosages respectively to water samples in the reactor which were stirred by the rotating of inner cylinder at 500 rpm of uniform speed for 2 min, followed by the slow stirring at different rotating speed for 10 min. Later, 10 minutes of settling time was required. After these procedures, the supernatants were drawn from the place of 210 mm deep under water surface. At last, the turbidities were measured by the turbidity meter (Hanna instruments, Italy).
Annulus gap meridianal plane of Taylor-Couette reactor is shown in
The mean velocity vector map of the meridianal plane in different rotation rates were obtained by PIV, as shown in
The instantaneous velocity vector maps of the meridianal plane were measured in different time and at constant rotation speed by PIV. From large amount of instantaneous velocity vector map, a regular change can be observed as long as the same rotation rate of the inner cylinder remains unchanged. The similar vortices periodically occur, and the wavelength is regular. Therefore, a periodical change of vortex state can be observed in these instantaneous velocity vector maps within a certain range. But, the differences between instantaneous velocities fields in one cycle decrease, and the periodicity of vortex state reappearance become shorter and shorter with the increase in rotation speed of the inner cylinder. At last, this periodical reappearance of vortex state disappear when R is greater than 40. A time sequence of eight instantaneous velocity field for R = 11.6 are shown in
The flocculation efficiencies of different PAC dosages for different rotating rate of inner cylinder were obtained as shown in
From
By using Equation (3), we calculated the azimuthal Reynolds numbers, Re, and the reduced-Reynolds number ratio R (=Re/Rec) for every rotating rate studied in this research, as shown in
It can be seen that the flow regimes [
Rotating rate (rpm) | Re | R | Flow regime |
---|---|---|---|
2 - 10 | 100 - 400 | 1 - 5 | TVF |
10 - 30 | 400 - 1500 | 5 - 20 | WVF |
30 - 60 | 1500 - 3000 | 20 - 40 | MWVF |
60 - 350 | 3000 - 17,000 | 40 - 200 | TTVF |
The same result as Liguang Wang’s are also obtained in our research, as shown in
The flocculation efficiencies reach the maximum values in the range between the 10 rpm and 30 rpm which falls within the WVF regime. But out of WVF regime, the comparatively low flocculation efficiencies are obtained;
Because the vortex in WVF is the closed vortex and periodically expands and contracts with time, WVF regime may be favorable for particles to collide each other, leading the higher flocculation efficiency.
When R is lower than that of WVF, the initial vortices are just beginning to form in this regime, which are non-closed or open vortices, leading the lower possibility of collision of particles and the lower flocculation efficiency.
With the increase in rotation speed of inner cylinder, the flow regime changes from WVF to TTVF, and the vortices change from closed vortices to no-closed vortices again which connect with each other, therefore the particles can move with water flow from one vortex to the neighboring vortex, thus decrease the possibility of collision of particles, leading the lower flocculation efficiencies.
We thank the financial support from the National Natural Science Foundation of China (No. 50878102).
Qing Chang,Yuhong Mao,Liyun Zeng,Changquan Yu, (2016) Flocculation Efficiency in Taylor-Couette Flow. Journal of Materials Science and Chemical Engineering,04,1-7. doi: 10.4236/msce.2016.41001