Analysis of flocculation in a jet clarifier. Part 1 – Global and local hydrodynamic analysis

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Highlights

  • PIV reveals a large circulation generated by the jet in the flocculation zone.

  • In this zone, the residence time is 10 times larger than the circulation time.

  • Instantaneous velocity gradients are measured and global ones are estimated.

  • Global velocity gradient G increases linearly with the jet flow rate.

  • The product G t, where t is the residence time, remains constant.

Abstract

Jet clarifier combines jet hydrodynamics, flocculation and settling in a unit operation. Generally, Camp and Stein G t parameter is recommended to evaluate clarifier efficiency, where G stands for a global velocity gradient and t a characteristic time scale (contact time). In this work, a quasi-two-dimensional jet clarifier is developed to make easier the hydrodynamic analysis of the flocculation zone of a jet clarifier. Measurements of instantaneous velocity field are performed by means of particle image velocimetry (PIV). PIV data are processed to visualise the strong circulation induced by the jet in the flocculation zone. Characteristic time scales related to macromixing are then extracted. Based on PIV data processing, local and instantaneous shear rate are estimated. The analysis of space averaged velocity gradient G is presented. The range of G is 2–15 s−1 whereas the residence time decreases from 4 to 1 h. Based on the hydrodynamic analysis, the parameter Gt is shown to be constant around 30,000 for different jet flow rates. Efficiency of such jet clarifier can thus be foreseen.

Introduction

In general, the target of surface water treatment consists in removing suspended particles that cause turbidity in water. Jet clarifier is the one type of solid contact clarifier, coupling flocculation and clarification (sedimentation zone) in a single unit (Degremont, 2007; Pani and Patil, 2007; Romphophak et al., 2016). In many research, the performance of the flocculator reactors were measured by residual turbidity (Garland et al., 2017). Normally, the turbidity removal efficiency of the free jet flocculator is about 70–75% (Randive et al., 2018). Nonetheless, the performance of the jet clarifier which is investigated in this study is about 80%. This jet clarifier was designed based on the criteria such as residence time, sedimentation and surface loading rate. Afterward, the trial and error method was used to reach the appropriate operating conditions by varying the inlet flow rates, the height of the sludge blanket, the gap ratio between the sedimentation wall section and the flocculation, and the diameter of the cone base diameter of truncated of flocculation zone; some of the appropriate conditions of this reactor's geometry were presented in Romphophak et al. (2016). Indeed, the scale of the jet clarifier presented in the previous paper is 4 times larger than the present scale, but the performance of the reactor in different scales is the same. However, the key phenomena that control the flocculation mechanisms are not clearly understood. Sobrino et al. (1996) also mentioned that the effluent residual turbidity was essentially independent of the flow rate and associated this result to a nearly constant value of Gt. The possible reasons were proposed without any evidence or proof. For example, Gt may be constant because when the flow increases through the chamber reactor, the mixing intensity increases, and the retention time decreases. The higher mixing intensity (gradient velocity) may be balanced by the shorter retention time, resulting in a nearly constant GT value. Furthermore, the authors based their analysis on head loss to estimate the velocity gradient. In the present study, the floc size distributions are independent of the flow rate too (see part 2 of this paper). The present analysis of the hydrodynamics of a jet clarifier is aimed at better understanding the physical phenomena explaining these independencies.

Commonly, the hydraulic flocculators have been designed based on a global parameter G t where G stands for the global velocity gradient and t stands for contact time (Camp and Stein, 1943; Pedocchi and Piedra-Cueva, 2005; Garland et al., 2017; Marques and Ferreira, 2017). In flocculation, the Camp and Stein criteria G t recommended to achieve efficient flocculation is usually in the following range:104<Gt<105

The analysis of G t in clear water and in the flocculation zone of a jet clarifier will constitute the final outcome of this paper; the global criteria G t will be highlighted by a local analysis of G t, where G will be the local shear rate and t is a hydrodynamic characteristic time.

Modelling of aggregation and break-up of flocs is out of the scope of this paper. However, it is important to recall how flocculation is related to hydrodynamics. One of the first attempts to quantify the collision rate of particles induced by hydrodynamics was proposed by von Smolan Smoluchowski (1916) in terms of local velocity gradient. Then, Camp and Stein (1943) extended Smoluchowski’s model of velocity gradient G. They also introduced a global parameter, the root mean square velocity gradient GRMS, in terms of power input by unit mass of liquid (W/kg). As reported by Pedocchi and Piedra-Cueva (2005), “the denomination velocity gradient has created some confusion about the physical interpretation of this parameter”. Indeed, the work of Camp and Stein has been revisited by many workers (among them Cleasby, 1984; Clark, 1985; Kramer and Clark, 1997). It is now accepted that the velocity gradient is defined as the square root of the viscous dissipation rate of kinetic energy (W/kg) divided by the kinematic viscosity. It is thus identical to the local shear rate and is defined as:G=γ˙=12trS2¯=12trS¯2+12tr(s'2¯)where S is the symmetric part of the velocity gradient tensor. Here, trS2¯ is an invariant. The first term on the r.h.s. is related to the square of mean velocity gradients whereas the second one stands for the average of the square of the fluctuating (turbulent) velocity gradients. These two terms are respectively related to the viscous dissipation of the mean flow kinetic energy and to the viscous dissipation of the turbulent kinetic energy. In turbulent flow, the first one is negligible compared to the viscous dissipation of the turbulent kinetic energy. Averaged over the whole tank or clarifier, the dissipated power is equal to the power input.

The present study focuses on hydrodynamics, in terms of local and instantaneous velocity field, induced by the jet in the flocculation zone of a jet clarifier. The two key words being “jet” and “clarifier”, the bibliography analysis will consider these two terms. However, in terms of application in chemical engineering and water treatment, the flocculation-clarifier issue will be predominant.

Jets are used in many industrial or environmental applications. In the past, jet flow hydrodynamics was addressed theoretically, experimentally and numerically. Schlichting (1979) was the pioneer to study jets. Bickley (1937) derived analytical solutions of jet flows; he demonstrated that the developing jet flow entrains external fluid, increasing the flow rate and decreasing the axial velocity, thus preserving constant momentum. Based on experiments, Miller and Comings (1957) showed that the jet decreases axially as the square root of the axial position along the jet (the origin being at the orifice outlet) and the jet size enlargement was shown to increase linearly with the axial position. These hydrodynamic phenomena will be investigated in our jet clarifier.

A jet is usually characterized by the Reynolds number at the injection. The Reynolds number is classically defined as:Re=Udνwhere U is the cross-averaged discharge velocity from the nozzle (m/s), d is the circular orifice nozzle internal diameter (m) and ν is the kinematic viscosity of the fluid (m²/s). Referring to Pearce (1966) conclusion, there is no turbulence below 500 and fully turbulent jet starts at 3000. Since in our study, the Reynolds number vary between 1000 and 4000, it corresponds to the transition from laminar to turbulent jet flow. Both jet structure and stability aspects of transition flows have also been reviewed by Mollendorf and Gebhart (1973). A submerged liquid jet from a circular orifice nozzle into a similar liquid exhibits three characteristics regions: (1) a developing flow region: about 10 nozzle diameters long; this region is called potential conic region; (2) a developed flow region: up to 100 nozzle diameters from the orifice; (3) a terminal region: above 100 nozzle diameters from the orifice.

It was reported that instabilities appear in the sheared layers induced by the submerged liquid jet. Downstream, mixing is controlled by the entrainment of surrounding liquid in the decelerating jet velocity region. In the developed flow region, the jet structure weakly depends on inlet conditions, in particular on discharge velocity profile. In our study, the discharge flow corresponds to laminar to turbulent flow pattern in the circular nozzle. In the developed flow region, the liquid flow induced by the jet exhibits radial enlargement. This was first addressed by Lee and Chu (1996), who assumed that the jet radial size increase was proportional to the discharge jet velocity. This gradual enlargement is related to a decrease of the mean velocity in the jet and to the entrainment of external fluid; thus, the analysis of the axial evolution of the jet radial size will be investigated.

The first issue of clarification is related to flocculation. Indeed, flocculation efficiency is related to mixing in the jet clarifier. The bibliographic analysis must thus focus on mixing induced by jets, in different geometries. In terms of mixing, Fossett and Prosser (1949) and Fossett (1951) reported inclined side-entry jet mixing of free turbulent jets in cylindrical tanks. Fox and Gex (1956) investigated both laminar and turbulent inclined side-entry jet regimes and concluded that the main phenomena controlling the mixing time was the momentum source injected by the jet in the tank. In terms of vertical jet mixer, studies were reported by Hiby and Modigell (1978) and by Lane and Rice (1982) in a hemi-spherical base, reporting shorter mixing times compared to flat base cylindrical tank. Maruyama et al. (1982) found that the mixing time in jet flow tank depended on the liquid depth, nozzle height, and nozzle angle, and the mixing time is a consequence of jet axis length. Maruyama et al. (1984) reviewed mixing induced in different geometries using horizontal, inclined and vertical jets. However, although global circulation was presented and global mixing time were determined, there was neither data nor information on the local phenomena controlling mixing.

Grenville and Tilton (1996) studied the free jet mixing time of the tank with H/D ≤ 1 where H is the fluid depth and D is the vessel diameter. They proposed that the mixing time had been correlated by turbulent kinetic energy dissipation rate (or power per unit mass). The turbulent kinetic energy dissipation rate at the end of the jet’s free path can be used to estimate the mixing rate and it controlled the mixing rate for the whole vessel. Then, Grenville and Tilton (1997) proffered the correlation based on the jet nozzle angle and compared their model with the circulation time model. They found that both models can be used to predict accurate mixing time in the tank and their previous model presented in 1996. Further, Grenville and Tilton (2011) continued their work by studying the mixing time in various tank geometries and found that their jet turbulence model fitted in the range of 0.2 < H/D < 3 and the ratio of mixing time to circulation time is not constant but rather depending on the ratio of fluid depth to diameter of the vessel.

Jayanti (2001) reported that the position of the “eye” of the circulation pattern induced by a jet is a key parameter for mixing and it depends on the tank geometry. Jayanti compared hemi-spherical base, ellipsoidal base, conical base with a half cone angle of 31° and conical base with a half cone angle of 58°. The best shape was found to be conical base with a half cone angle of 31°. In this case, the “eye” of the recirculation pattern is half the overall height, the recirculation is quite strong and there is no low velocity region. This conclusion probably contributes to explain the efficiency of the present jet clarifier since flocculation zone corresponds to a divergent (2D cone). Wasewar (2006) investigated design of jet mixing tank. His review summarizes different studies of jet mixed tank parameters (tank geometry, jet configuration, jet velocity, jet diameter, jet flow rate and fluid properties) to get an optimum design. He pointed out that mixing time is an important parameter to design jet tank devices.

Perumal and Saravanan (2012) and Randive et al. (2018) investigated jet mixing; they pointed out that the difference between jet and bulk liquid velocity creates a turbulent mixing zone along the jet boundary. In this mixing zone, some part of the surrounding fluid is circulated at high velocity and create a circulation loop, thus leading to mix the bulk of the liquid. This kind of circulation loop induced by the jet will be investigated in this paper. Randive et al. (2018) reviewed the jet mixing in the flocculation process and summarized several models to estimate the mixing time in terms of other parameters such as jet velocity, jet diameter, jet path length, and tank diameter and height.

Kennedy et al. (2018) studied the effect of the distance between injection and suction ports on the control mixing time of submerged recirculation jets. They found that the distance between the ports can be used to control mixing time at the same value of injection velocity and an empirical correlation to predict the mixing time under short-circuiting conditions of the flow is dominant, which retains the same dependence of mixing time on the injection velocity and the tank diameter.

Garland et al. (2017) analysed the effects of Gt on turbidity removal by hydraulic flocculator, indicating better performance when a floc blanket had been formed. They concluded that appropriate mixing time is a factor that can be used to limit the size of the clarifier. In our paper, since only clear water hydrodynamics is investigated, floc blanket will not be accounted for.

In order to investigate the hydrodynamics of the new jet clarifier, PIV experiments will be presented and discussed, both in terms of jet characteristics and in terms of flow structure leading to the estimation of Gt criteria.

Section snippets

Set up

The laboratory pilot was designed to investigate local hydrodynamic of the jet clarifier. A pseudo-two-dimensional jet clarifier was designed with 56 cm. high, 95 cm long, and 10 cm thickness, which is named as a flat quasi-bidimensionnal (Q2D) clarifier. The Q2D jet clarifier was constructed using Plexiglass (PMMA) (1 cm thick) enabling velocity measurement with especially the flocculation zone, a cone-shape, inside the reactor. The liquid volume in the pilot is 42 L. Fig. 1 illustrates the

PIV results in the flocculation zone

Results concern the hydrodynamics of the flocculation zone (estimated to 7 L volume), located in the vertical divergent of the jet clarifier (Fig. 1). In this section, results are organised as follows: velocity fields in zones 1 and 2 of the pilot (Fig. 2) are plotted, exhibiting a large circulation. Circulation flow rates are estimated as well as circulation time that are compared to residence time in this zone. The characteristic shape of the jet is also investigated, in terms of vertical

Discussion on hydrodynamics for flocculation

In the section, both local-instantaneous and global (time and space averaged) velocity gradient are addressed.

On Fig. 7, the vertical profiles of four characteristic variables are plotted: the local mean vertical velocity, the viscous dissipation rate of kinetic energy, the Kolmogorov scale and the velocity gradient (shear rate). Fig. 7(a) corresponds to the vertical profile of mean velocity along the axis (X = 0), normalised by the inlet velocity. Clearly the profiles are identical, except in

Conclusion

In order to understand the good efficiency of a jet clarifier, a hydrodynamic study was led. In order to use PIV technique for local analysis, a quasi-bidimensional pilot was designed. Three flow rates were investigated which correspond to residence time from 1 h to 4 h. The local hydrodynamic analysis was limited to the flocculation zone (fields 1 & 2 of Fig. 2) near the jet inlet where the global velocity gradient G is higher. Results concerning the hydrodynamics of the flocculation zone

Declaration of interests

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.

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.

Acknowledgements

This work was supported by Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0152/2558) under Thailand Research Fund (TRF) and French Embassy in Thailand. Funding last year of Ploypailin Romphophak PhD was supported by the team Transfer-Interface-Mixing from Toulouse Biotechnology Institute in Toulouse.

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