Nessrin Manaa

Awatef Abidi

Patrice Estellé
email: patrice.estelle@univ-rennes1.fr

Mohammed Naceur

Mohammed Naceur Borjini

Numerical simulation of three-dimensional thermo-solutal convection of micropolar multi-walled carbon nanotubes water nanofluid stabilized by lignin and sodium polycarboxylate

Keywords: thermo-solutal convection, three-dimensional, micropolar CNT-water nanofluid, surfactant

Numerical simulation of three-dimensional thermo-solutal convection of micropolar multi-walled carbon nanotubes water nanofluid stabilized by lignin and sodium polycarboxylate

Introduction

Over the last years, the demand on energy is become more intensive due to the extensive growth of industry and population. In fact, energy is considered as essential element for human being because her daily activities which need energy. The one of major energy which is needed in consuming process in industrial applications is double diffusive natural convection. It exist many applications in industry and research where the phenomena of double diffusive natural convection is present such as the crystal growth for the manufacture of semiconductors and electronics equipments cooling, solar collectors, home ventilation and heat exchangers. Moreover, utilizing nanofluid is one of the new methods for conservation energy during natural convection. These fluids are manufactured by the dispersion of nanoparticles in conventional heat transfer fluids. Itexists many types of nanoparticles used in nanofluids that differ in nature, such as metallic (Al, Cu, Ag...), oxide (Al 2 O 3 , TiO 2 , CuO…) and carbon-based materials. Putra et al. [START_REF] Putra | Natural convection of nano-fluids[END_REF] investigated experimentally the natural convection of nanofluid in a horizontal cylinder filled with two types of nanoparticles CuO and Al 2 O 3 .

They obtained a decrease in heat transfer rate with the enhancement in nanoparticles' concentrations. Khanafer et al. [START_REF] Khanafer | Buoyancy-driven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids[END_REF] carried out a numerical investigation on natural convection with Cu nanofluid and noticed heat transfer increase with an increase in nanoparticles' volume fraction. Jou and Tzeng [START_REF] Jou | Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures[END_REF] numerically examined the natural convection in a twodimensional enclosure, filled by Cu/water nanofluid for various pertinent parameters such as Rayleigh number, aspect ratio, buoyancy parameter and nanoparticles's volume fraction.

Enhancement in heat transfer was shown to be more efficient with nanofluid than with pure fluid. Abu Nada et al. [START_REF] Abu-Nada | Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids[END_REF] carried out numerical investigations considering different nanofluids based on Al 2 O 3 , TiO 2 , Cu and Ag, in horizontal annuli. They reported the dependence of heat transfer performance following the type of nanofluid used. Öztop and Abu Nada [START_REF] Oztop | Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids[END_REF] carried a numerical investigation of heat transfer and fluid flow due to buoyancy forces in a partially heated enclosure filled with different types of nanofluids. They found that the average Nusselt number increases with the nanoparticles volume fraction.A numerical study of forced convective heat transfer in horizontal tubes filled with Al 2 O 3 /water nanofluid was investigated by Minea [START_REF] Minea | Uncertainties in modeling thermal conductivity of laminar forced convection heat transfer with water alumina nanofluids[END_REF]. The author established that the heat transfer coefficient of water-based Al 2 O 3 nanofluids is increased compared to that of pure water. Bouhalleb and Abbassi [START_REF] Bouhalleb | Numerical investigation of heat transfer by CuO-Water nanofluid in rectangular enclosures[END_REF] numerically studied the natural convection of CuO-water nanofluid in inclined cavity differentially heated. They showed that the efficiency of heat transfer is enhanced by the addition of nanoparticles into base fluid. However, there is acritical solid volume fraction which maximizes the heat transfer rate. Minea et al. [START_REF] Minea | NanoRound: A benchmark study on the numerical approach in nanofluids' simulation[END_REF] carried out a benchmark study on the numerical approach in nanofluids' simulation. They compared different numerical approaches with experimental studies, concluding that multiphase model gives the most reliable results for nanofluid flow in long straight pipe. Purusothaman et al. [START_REF] Purusothaman | Three dimensional numerical analysis of natural convection cooling with an array of discrete heaters embedded in nanofluid filled enclosure[END_REF] carried out a numerical analysis aboutnatural convective heat transfer ina three dimensional rectangular enclosure filled with nanofluid and in the presence of an array of discrete heaters. They founded that the averaged Nusselt number increases with increase in both the Rayleigh number and the nanoparticle solid volume fraction. Selimefendigil and Öztop [START_REF] Selimefendigil | Mixed convection of nanofluids in a three dimensional cavity with two adiabatic inner rotating cylinders[END_REF] investigated numerically the three dimensional mixed convection in a cubic enclosure with two rotating cylinders and containing various types of nanofluids. The average heat transfer is enhanced with nanoparticles, the higher rate being achieved for Cu-water nanofluid compare to Al 2 O 3 -water nanofluid and TiO 2 -water nanofluid. A numerical study on laminar double diffusive natural convection in a square cavity was performed by Esfahani and Bordbar [START_REF] Esfahani | Double diffusive natural convection heat transfer enhancement in a square enclosure using nanofluids[END_REF]. Different types of nanofluid were used and the effect of pertinent parameters (Rayleigh number, Lewis number, buoyancy fraction and nanoparticles volume fraction) on heat and mass transfer rates was explored. Also, Parvin et al. [START_REF] Parvin | Double diffusive natural convection in a partially heated enclosure using nanofluid[END_REF] numerically investigated double-diffusive natural convection in a partially heated enclosure filled with Al 2 O 3 /water nanofluid. It is noticed that the Rayleigh number and nanoparticles volume fraction influence on the distributions of isotherms and iso-concentrations. Chen et al. [START_REF] Chen | Double diffusion natural convection in a square cavity filled with nanofluid[END_REF] thoroughly discussed the influence of nanoparticles' volume fraction on Nusselt and Sherwood numbers for both laminar and turbulent regimes. In fact, they concluded that the effects adding nanoparticles into base fluid are totally differentbetween the laminar regimes and turbulent regimes. Recently, a study was conducted by Aly and Raizah [START_REF] Aly | Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method[END_REF] on double diffusion and mono diffusion natural convection with nanofluids using incompressible smoothed particle hydrodynamics method. They founded that the increase Soret number accompanied by a decrease in Dufour number result in an enhancement inheat transfer rate and a reduction in mass transfer rate.Among all nanoparticles available for producing nanofluids, carbon nanotubes (CNT) are more recommending than other traditional nanoparticles because of their relatively low density and very high thermal conductivity.Wen and Ding [START_REF] Wen | Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids)[END_REF] studied the effective thermal conductivity of aqueous suspensions of MWCNTs.They used the sodium polycarboxylate as surfactant to stabilize the nanofluids. They obtained an enhancement of thermal conductivity when the nanoparticles volume concentrationincreases, and the dependence was nonlinear even at very low concentrations. They founded that an enhancement in temperature increases the effective thermal conductivity of nanofluid. Jiang el al. [START_REF] Jiang | Measurement and model on thermal conductivities of carbon nanotube nanorefrigerants[END_REF] investigated the characteristics of CNT nano-refrigerants and their thermal conductivity. They founded that the thermal conductivities of CNT nanorefrigerants are much higher than those of CNT-water nanofluids and they increase significantly with the increase of the nanoparticles volume fraction. Halelfadl et al. [START_REF] Halelfadl | Optimization of thermal performances and pressure drop of rectangular microchannel heat sink using aqueous carbon nanotubes based nanofluid[END_REF] discussed the optimization of a rectangular microchannel filled with aqueousmulti-walled carbon nanotubes (MWCNTs)/water nanofluid as coolant. They showed that using nanofluid induces a decrease of the total thermal resistance and leads to an enhancement of thermal performances at high temperatures. Estellé et al. [START_REF] Estellé | Thermal conductivity of CNT water based nanofluids: Experimental trends and models overview[END_REF] investigated the thermal conductivity of carbon nanotube water-based nanofluids. They studied the effect of the volume fraction of nanoparticles, temperature, nanoparticles aspect ratio and different types of surfactant. They observed an enhancement of thermal conductivity of nanofluid at low volume fraction.

However, this enhancement is weakly affected by the carbon nanotubes aspect ratio and the type of surfactant used. A study of the effect of lignin as surfactant on viscosity and thermal conductivity of CNT/water-based nanofluids was investigated by Estellé et al. [START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids:Impact on viscosity and thermal conductivity[END_REF]. They compared the effect of lignin on the viscosity and thermal conductivity of CNT/water nanofluid with the effect of sodium polycarboxylate. They noticed that the thermal conductivity of nanofluid increase with the nanoparticles volume concentration. Rahman et al. [START_REF] Rahman | Unsteady natural convection and statistical analysis in a CNT-water filled cavity with nonisothermal heating[END_REF] numericallyinvestigated the natural convective heat transfer and fluid flow in a square cavity filled with CNT-water nanofluid with non-isothermal heating. They founded that there is an optimum value for nanoparticles volume fraction to control heat transfer, temperature distribution and flow field. Job and Gunakala [START_REF] Job | Unsteady MHD Free Convection Nanofluid Flows Within A Wavy Trapezoidal Enclosure With Viscous And Joule Dissipation Effects[END_REF] investigated the unsteady MHD natural convection flows of two types of nanofluid Al 2 O 3 /water and SWCNT/water within a symmetrical wavy trapezoidal enclosure with viscous and Joule dissipation effects. They studied the effect of time, Hartmann number, wall amplitude, and solid volume fractionon the fluid flow and heat transferrate. They showed that the SWCNT/water nanofluid has a higher heat transfer rate at the wavy bottom wall than the Al 2 O 3 /water nanofluid. Estellé et al. [START_REF] Estellé | Natural convection of CNT water-based nanofluids in a differentially heated square cavity[END_REF] investigated theoreticallythe natural convection in a square cavity partially heated filled with CNT water-based nanofluids. They analyzed the effect of the average temperature and the nanoparticles volume fraction, driving temperature between hot and cold walls and role of surfactant. They founded that the Nusselt number of nanofluids is decreased with the increase of the volume fraction of nanofluid, which is related to non-Newtonian behavior of nanofluids. Minea and Estellé [START_REF] Minea | Numerical study on CNT nanofluids behavior in laminar pipe flow[END_REF] carried out a numerical study of the heat transfer behavior of carbon nanotubes nanofluids under laminar forced flow in horizontal pipe. They evidenced that the convective heat transfer coefficient of nanofluid is better for low Re number and higher nanoparticles volume fraction. Kolsi et al. [START_REF] Kolsi | Control of natural convection via inclined plate of CNT-water nanofluid in an open sided cubical enclosure under magnetic field[END_REF] performed a computational analysis about an open cubic cavity filled with CNT-water nanofluid. This numerical analysis is performed for different governing parameters as Rayleigh number, nanoparticles volume fraction, Hartmann number and inclination angle of the fin. It is concluded that heat transfer rate and fluid flow dependsonthese parameters. Al-Rashed et al. [START_REF] Kolsi | Second law analysis of natural convection in a CNT-Water nanofluid filled inclined 3D Cavity with incorporated Ahmed Body[END_REF] carried out a numerical study of entropy generation inside an inclined cubical cavity differentially heated filled with CNT/water nanofluid. They analyzed the effects of Rayleigh number, nanoparticles volume fraction, inclination angle of cavity and thermal conductivity ratio on entropy generation. Rahimi et al. [START_REF] Rahimi | Experimental and numerical study on heat transfer performance of three-dimensional natural convection in an enclosure filled with DWCNTs-water nanofluid[END_REF] conducted a numerical and experimental analysis on heat transfer performance of 3D natural convection in a cubic cavity filled with double-walled CNTs-water nanofluid at different temperature differences between side hot and cold walls. In this work, the thermo-physical properties such us the thermal conductivityand the dynamic viscosity, of the double-walled CNTs-water nanofluid are experimentally evaluated. They revealed that the changein temperature difference influences the temperature distribution within the cavity.

However, the enhancement of nanoparticles volume concentration has no significant effect on the temperature. Also, they demonstrated that it exist an optimum value of solid volume fraction forhighest value of average heat transfer coefficient and Nusselt number. Over this optimum,both parameters are deteriorated.

The theory of Enrigen [START_REF] Eringen | Theory of micropolar fluids[END_REF] can be used to elucidate fluid particles' micro-motions which cannot be explained by the classical models. In fact, physically, fluid particles may expand, contract, rotate about their own axis or may even change their shape due to the shear stress applied on them. So, the micropolar fluid theory can be valuable to explore fluid behavior of polymer fluids, solidification of liquid crystals, cooling of a metallic plate in a bath, exotic lubricants, colloidal systems, and biological fluids, for which the theory of Navier-Stokes is inadequate to describe the impacts of the microstructures on fluid motion.

Description and applications of natural convection with micropolar fluid in enclosures have been studied in the following papers. Aydin and Pop [START_REF] Aydın | Natural convection from a discrete heater in enclosures with a micropolar fluid[END_REF] performed a numerical study of a steady natural convective heat transfer of micropolar fluids in a square cavity. They identified that an increase of the micropolar parameter reduced the heat transfer rate. Zadravecet al. [START_REF] Zadravec | Natural Convection Of Micropolar Fluids in an Enclosure With Boundary Element Method[END_REF] carried out a numerical investigation of natural convection of a micropolar fluid within an enclosure. It was obtainedthat the local and average Nusselt numbers decrease with the enhancement of the micropolar parameter. Jena et al. [START_REF] Jena | Transient buoyancy-opposed double diffusive convection of micropolar fluids in a square enclosure[END_REF] extracted the numerical solution of the transientbuoyancy-opposed double diffusive natural convection of a micropolar fluid. They observed that the flow strength and heat and mass transfer rates are deteriorated for growing values of the micropolar parameters. Abidi and Borjini [START_REF] Abidi | Effects of Microstructure on Three-Dimensional Double-Diffusive Natural Convection Flow of Micropolar Fluid[END_REF] discussedthe effect of micro-constituents in micropolar fluid on the three-dimensional doublediffusive natural convection. They evidenced the deterioration in three-dimensional character of the flow with a considerable reduction in heat and mass transfer rates with an increase in the micropolar parameter.

The rotating micro-constituents' effects in nanofluids should be judiciously exploited to understand the behavior of fluid flow effectively. Bourantas and Loukopoulos [START_REF] Bourantas | Modeling the natural convective flow ofmicropolar nanofluids[END_REF] theoretically examined the natural convection of micropolar nanofluids. One of the main objectives of this work wasto study the effect of the micropolar model on heat transfer rate.

They founded that the increase in nanoparticles micro-rotation caused a decrease in the heat transfer rate. Hashemi et al. [START_REF] Hashemi | Cu-water micropolar nanofluid natural convection within a porous enclosure with heat generation[END_REF] numerically investigated micropolarCu/water nanofluid natural convection. A heat generation source in a porous medium was considered in this case.

They highlighted that the rotational strength of vortices enhances with the increase in the micropolar parameter. Hussanan et al. [START_REF] Hussanan | Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil[END_REF] used five types of oxide nanoparticles dispersed in water, kerosene and engineoilto explore the unsteadynatural convection flow of micropolar nanofluids past a vertical plate. They obtained that the type of nanoparticles and the base fluid significantly influence heat transfer rate and flow behavior.The effect of the magnetic field on natural convection in a micropolar nanofluid was investigated by Bourantas and Loukopoulos [START_REF] Bourantas | MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid[END_REF]. The study focused on an inclined rectangular cavity and reveals that the presence of nanoparticles influences the thermal properties of the base fluid.The mixed convection in a lid-driven cavity filled with micropolar nanofluid was analyzed by Ahmed et al. [START_REF] Ahmed | Mixed convection from a discrete heat source in enclosures with two adjacent moving walls and filled with micropolar nanofluids[END_REF].They founded that the average Nusselt number along the heat source increases when the solid volume fraction increases. Nering and Rup [START_REF] Nering | The effect of nanoparticles added to heated micropolar fluid[END_REF] numerically analyzed the heat transfer of micropolar nanofluids with two different base fluids: ethylene glycol and water. They obtained that the maximum heat transfer enhancement parameter for nanofluid without micropolar properties appears for Cu/ethylene glycol nanofluid. On the other hand, they observed thatAl 2 O 3 /water nanofluid has a greater value of heat transfer enhancement. Izadi et al. [START_REF] Izadi | Natural convection of CuO-water micropolar nanofluids inside a porous enclosure using local thermal non-equilibrium condition[END_REF] studied the natural convection of a micropolar nanofluid inside a porous cavity with the use of a thermal non-equilibrium model. They founded that the increase of micropolar parameter induces a reduction of the thermal resistance of the fluid phase. Rashad et al. [START_REF] Rashad | Mixed convection from a discrete heater in liddriven enclosures filled with non-Newtonian nanofluids[END_REF] reported the outcomes of a computational investigation on micropolar nanofluid natural convection inside an enclosure with a heatingsource located at the bottom. Their results indicate that an increase in the micropolar parameter causes a reduction in the local Nusselt number. Also they concluded that as the nanoparticle volume fraction increases, the rate of heat transfer increases. Abidi et al. [START_REF] Abidi | Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid[END_REF]

Thermophysical properties of multi-walled carbon nanotube nanofluid

For comparison purpose with nanofluids, water which is the base fluid of nanofluids was taken as a reference. The thermo-physical properties of water used for the simulations are reported in [START_REF]Therme-Excel: Physical characteristics of water at the atmospheric pressure[END_REF]. The density, the heat capacity, the thermal conductivity, the thermal expansion coefficient and the dynamic viscosity of water are respectively equal to 998.205 kg m -1 , 4182 J kg -1 K -1 , 0.6 W m -1 K -1 , 0.00021 K -1 and 1.003 mPa s.

In this study, it is considered carbon nanotubes with density of 1800 kg m -3 and purity of 90% and 9.2 nm and 1.5 µm in average diameter and length, respectively, dispersed in a mixture of water and surfactant. To improve the dispersion and stability of multi-walled CNT within water and to reduce clogging and the sedimentation with time, it was used two types of surfactants lignin and sodium polycarboxylate. The preparation of nanofluid was reported in [START_REF] Estellé | Thermal conductivity of CNT water based nanofluids: Experimental trends and models overview[END_REF][START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids:Impact on viscosity and thermal conductivity[END_REF][START_REF] Estellé | Natural convection of CNT water-based nanofluids in a differentially heated square cavity[END_REF]. The volume fraction of carbon nanotubes under consideration ranges from 0.0055 to 0.557%. Density, thermal conductivity, viscosity at 20°C were experimentally determined in [START_REF] Estellé | Thermal conductivity of CNT water based nanofluids: Experimental trends and models overview[END_REF][START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids:Impact on viscosity and thermal conductivity[END_REF][START_REF] Estellé | Natural convection of CNT water-based nanofluids in a differentially heated square cavity[END_REF] from well-designed procedures while heat capacity was theoretically determined neglecting heat capacity of surfactants. All these results are shown in Fig. 2 and used in the present numerical simulations.

In the following, nanofluids produced with lignin are labeled N2. N3 is used for nanofluids obtained with sodium polycarboxylate as a surfactant. To make easier the implementation of thermophysical data of nanofluids in the numerical simulation and program [START_REF] Mohd-Ghazali | Thermal and hydrodynamic performance of a microchannel heat sink with carbon nanotube nanofluids[END_REF], the following formulas of thermophysical properties of nanofluids have been adjusted on experimental data. The thermal expansion coefficient of nanofluids was calculated from the following equation [START_REF] Khanafer | Buoyancy-driven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids[END_REF] as:

(

Where the thermal expansion coefficient of carbon nanotubes at 20°C was taken as 2.10 -5 [START_REF] Estellé | Natural convection of CNT water-based nanofluids in a differentially heated square cavity[END_REF].

Governing Equations

The dimensionless governing equations are thefollowings:

(

The following non-dimensional variables are used for the normalization of the required governing equations (2) (3) (4) ( 5) and ( 6):

, , , ,

and
The vector of micro-rotation may be presented as follows: [START_REF] Agarwal | Finite element solution of non-steady three dimensional micropolar fluid flow at a stagnant point[END_REF], Takhar et al. [START_REF] Takhar | Mixed convective non-steady 3dimensional micropolar fluid flow at a stagnation point[END_REF], and Chamkha et al. [START_REF] Chamkha | Three dimensional micropolar flow due to a stretching flat surface[END_REF]).

) 0 , ' , ' ( ' 2 1 H H H  (Agarwal et al.
In these equations, the dimensionless Pr, Le, Ra, N and K numbers are respectively defined as

The vorticity-vector potential formulation is used in the present study to eliminate the pressure term and makes easier the numerical treatment. The vorticity and vector potential are respectively defined by the following two relations: and .

The system of governing equationsof the phenomenonis

(7) (8) (9)
The local Nusselt and Sherwood numbers on the isothermal walls are defined by:

(12) (13)
The average Nusselt and Sherwoood numbers, on the isothermal walls of the enclosure are defined as follows:

z y Nu u N      1 0 1 0 (14) z y Sh Sh      1 0 1 0 (15)
For each time step, the following convergence criterionissatisfied: [START_REF] Jiang | Measurement and model on thermal conductivities of carbon nanotube nanorefrigerants[END_REF]

Boundary conditions

The current numerical simulations employ the following boundary conditions:

Temperature and concentration:

(17) (18) (19)
           (22)
At z=0 and z=1 :

0 , z U , z U 3 1 2 2 1            (23)
Vector potential: At x=0 and x=1 :

0 3 2 1         x ( 24
)
At y=0 and y=1:

0 3 2 1         y (25)
At z=0 and z=1 :

0 3 2 1      z    (26)
Velocity on all walls:

0 3 2 1    U U U (27)
Simulations are accomplished for strong concentrated suspensions (Guram and Smith [START_REF] Guram | Stagnation flows of micropolar fluids with strong and weak interactions[END_REF]). It characterized the case in which the microelements in the vicinity of the wall surface are incapable to rotate. Thus, the boundary conditions for micro-rotation vector are given as follows:

0 : 0,1 = z and 0,1 = y ; 0,1 = At x  H ( 28
)

Numerical procedure and code validation

The FORTRAN language was used to write the numerical program and solve the mathematical model described above. The governing equations (( 7)-( 11)) were discretized using the finite volume method based on the central-difference scheme andsolved using the successive relaxation iteration scheme. Thegrids are uniform in all directions, and additional nodes are added onboundaries. A time-step of 10 -4 and spatial mesh of 51×51×51 was used during the numerical simulations and the convergence criterion given in equation ( 16) was satisfied. We used an Intel core i5 microprocessor for the numerical simulation, the time of execution was about7 h for Ra= 10 5 . Hence, the (51×51×51) grid was estimated to be appropriate for the present study at least for Ra 10 5 since it permits a good compromise between the computational cost (a significant reduction of the execution time) and the accuracy of the obtained results, as shown above in Table 2.

The finite volume method consists in defining mesh nodes inside the computation domain and in constructing a control volume around each node. The space is divided into a finite number of elementary volumes. The main nodes are located in the center of each volume and additional nodes on the boundaries of the domain. A grid independence study has been first carried out such that the exact number of grids for the present simulations is wisely determined. The grid independency analysis is presented in Table 2. The values of average Nusselt and Sherwood numbers on the hot wall at different grid sizes are calculated for K=1, Ra=10 5 and φ=0.00055. A 51×51×51 uniform grid is found to meet the requirements of both the grid independency study and the computational time limits. The percentages quoted in Table 2 represent relative errors corresponding to the above quoted value. The validation of our three-dimensional numerical code of natural convection of nanofluid was also performed against the results generated by Kolsi et al. [START_REF] Kolsi | Computational Analysis of Three-Dimensional Unsteady Natural Convection and Entropy Generation in a Cubical Enclosure Filled with Water-Al 2 O 3 Nanofluid[END_REF] for water-Al 2 O 3 nanofluid as shown in Fig. 3. It can be seen from this figure that the solution of the present numerical code is in excellent agreement with the numerical results from Kolsi et al. [START_REF] Kolsi | Computational Analysis of Three-Dimensional Unsteady Natural Convection and Entropy Generation in a Cubical Enclosure Filled with Water-Al 2 O 3 Nanofluid[END_REF].

Afterwards, the proposed three-dimensional nanofluid model that takes into account the nanoparticles microrotation is validated against experimental data of Putra et al. [START_REF] Putra | Natural convection of nano-fluids[END_REF]. To that end, a two-dimensional version of the present code is derived and the results are compared to those of Putra et al. [START_REF] Putra | Natural convection of nano-fluids[END_REF] for natural convection of Al 2 O 3 /water nanofluid.

Figure 4illustrates that the experimental data and our numerical results reveal similar trends. We realized a bi-dimensional natural convection of Al 2 O 3 /water nanofluid simulations.

One can cite, for example for Ra= , the difference between our numerical results and experimental results of Putra et al. [START_REF] Putra | Natural convection of nano-fluids[END_REF] is about 22.8% at K=1 then it is decreased to 2.26% at K=3. It can be clearly observed that the maximum difference between experimental study and our results for K=3 does not exceed 3.89% for all the Rayleigh numbers considered. Evidently, as the microrotation parameter K increases our numerical results tend to the experimental data. Therefore, this evidences the role of the nanoparticles microrotation and the need to consider its influence in the proposed simulations.

As a summary, in all validations, a reasonable agreement can be established between the present investigation results and those from earlier published works [START_REF] Putra | Natural convection of nano-fluids[END_REF][START_REF] Sezai | Double diffusive convection in a cubic enclosure with opposing temperature and concentration gradient[END_REF][START_REF] Kolsi | Computational Analysis of Three-Dimensional Unsteady Natural Convection and Entropy Generation in a Cubical Enclosure Filled with Water-Al 2 O 3 Nanofluid[END_REF]. versus Rayleigh number with increasing vortex viscosity parameter K for φ = 4%

Results and discussion

The thermo-solutal natural convection in a cubic cavity filled with a multi-walled CNT/water micropolar nanofluid stabilized with two types of surfactants is computationally investigated. Water solution was considered as the base fluid for all simulations. The Prandtl and Lewis numbers are fixed respectively equal to Pr=7 and Le=1 (Aly and Raizah [START_REF] Aly | Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method[END_REF]). The simulations were carried out for the range of Rayleigh numbers (10 4 ≤ Ra ≤ 10 6 ), micropolar parameter (0 ≤ ≤ 10), buoyancy ratio (-1 ≤ ≤ 0),and nanoparticle volume fractions (0.055% ≤ φ ≤ 0.557%), to investigate the effects of various micropolar nanofluid on flow dynamics, heat and mass transfer characteristics. The effect of types of surfactants used to the stability of nanofluid has been investigated. Moreover, the influence of micropolar /nonmicropolar model is analyzed by analyzing streamlines, isotherms, isoconcentrations and average Nusselt and Sherwood numbers. For more clarification, Fig. 6 elucidates the variations of the horizontal and vertical velocity components for z = 0.5 and Ra=10 5 obtained by usingN2/N3 nanofluid with the micropolar model to evidence the consequence of nanoparticles concentration increase. Based on this figure, the amplitudes of the velocities U 1 (0.5, y 0.5) and U 2 (x, 0.5, 0.5) are ameliorated when is less than the critical value and then are deteriorated when it exceeds this value. Similarly, it can also be seen in Fig. 6 that when the N2 nanofluid is employed, the intensity of the principal flow is higher than for N3 nanofluid. This can be explained by the lower dynamic viscosity of N2 compared to N3. the maximum transverse velocity is improved by increasing φ to the critical value then the velocity tends to decrease. Also, it is clearly noted that N2 have higher transverse velocity compared to N3. For example, for φ=0.0055% it exists a 27.63 % difference between the two cases. In addition, it isinteresting to note that the non-miropolar nanofluid (K=0) has the highest maximum transverse velocity compared to the micropolar nanofluids (K≠0) for all the considered values of nanoparticles volume fraction. It is noticed that for the two types of surfactants used, the average Nusselt and Sherwood numbers increase in the area where the value of the volume fraction of nanoparticles is less than its critical value. This is because the thermal performance of water solution is improved by the addition of nanoparticles. Afterwards, the heat and mass transfer rates decrease in the area where the value of the nanoparticles volume fraction is greater than its critical value due to the predominant influence of viscosity over thermal properties. It can be seen also from Fig. 8, for the case where the surfactant lignin is used, the average Nusselt and Sherwood numbers are greater than in the case of the surfactant sodium polycarboxylate is employed. At therather low buoyancy ratio , the flow is mainly dominated by the thermal buoyancy force, so that the main flow direction is clockwise in the x-y plane. As the buoyancy ratio is It is understood from this figure that both and have a quasi-similar profile for both micropolar and non-micropolar N2/N3 nanofluid models. As the N is decreased in a negative direction until N=-1, both the values of and show declining tendency.

The average heat and mass transfer rates are higher for K=0 when compared to micropolar nanofluid (K≠ 0) irrespective of the used surfactants. This phenomenon reflects the fact that increasing the value of vortex viscosity parameter results in an enhancement of the total viscosity in fluid flow and hence the heat and mass transfer rates are retarded.

It is alsoimportant to note that the comparison between figures of Lignin (N2) and sodium polycarboxylate (N3) reveals that employing a nanofluid stabilized with Lignin (N2)

ameliorates the average Nusselt and Sherwood numbers more than that of sodium polycarboxylate (N3). and sodium polycarboxylate (N3). Regardless of the nanoparticles' volume fraction, the heat and mass transfer increase with the increase in values of Ra.It can be observed that the heat and mass transfer increase in the area where the value of the nanoparticles volume fraction is less than a critical value. This is because the thermal performance of water solution is improved by the addition of nanoparticles. Afterwards, the heat and mass transfer rates decrease in the area where the value of the nanoparticles volume fraction is greater than the critical value due to the predominant influence of viscosity over thermal properties. This figure shows that for both types of surfactant, the maximum of transversal velocity increases by increasing Ra. In addition, the three-dimensional character of the flow depends on nanoparticles volume fraction. In fact, it increases when is less than a critical value, then U 3max decreases when is higher than their critical value.

Conclusion

Three-dimensional computational analysis has been performed toinvestigate the double diffusive natural convection of micropolar multi-walled carbon nanotubes-water nanofluids stabilized with two types of surfactants lignin and sodium polycarboxylatein a differentially heated cubical enclosure for different governing parameters (Rayleigh number, micropolar parameter, and nanoparticles volume fraction). This numerical work has been performed considering real experimental data for thermophysical properties of multi-walled carbon nanotubes-water nanofluids. The main findings of this numerical analysis can be summarized as follows  The multi-walled carbon nanotubes-water nanofluid stabilized with lignin exhibits more heat and mass transfer rates when compared to multi-walled carbon nanotubes-water nanofluids stabilized with sodium polycarboxylate. So using lignin as a surfactant is better than using sodium polycarboxylate.

  Fig.1 (a) Schematic of the considered problem, (b) Mesh surfaces

Fig. 2

 2 Fig. 2 Thermophysical properties of CNT nanofluids at 20°C with two types of surfactants: (a) thermal conductivity, (b) density, (c) dynamic viscosity and (d) heat capacity

Figure 1 (

 1 b) displays the mesh configuration of the present physical domain.

Fig. 3 6 )Fig. 4

 364 Fig. 3 Comparison of the streamlines with the results of Kolsi et al. [50] (Pr=6.2, and Ra=10 6 )

Figure 5 Fig. 5

 55 Figure5displays, projections of flow lines in the main plane (z=0.5) for various nanoparticles volumes fractions for micropolar/non-micropolar nanofluid stabilized with Lignin (N2) and sodium polycarboxylate (N3). In the two cases, the main flow direction is clockwise in the x-y plane. Also, it can be mentioned that the intensity of the flow depends on the volume fraction of the nanoparticles. Indeed, for φ≤0.055% the intensity increases while

Fig. 6

 6 Fig. 6 Variation of components of velocity U 1(0.5,y,0.5) and U 2(x,0.5,0.5) versus different nanoparticles volume fraction, for N2 and N3 nanofluid, for Ra=10 5 , K=1 and N=-0.2.

Figure 7

 7 Figure 7 shows the variations of maximum transverse velocity with the nanoparticle's volume fraction for micropolar/non-micropolar nanofluid stabilized with Lignin (N2) and sodium polycarboxylate (N3). Thus, the effects of nanoparticles' volume fraction on the three-dimensional flow are explored. This figure shows, irrespective of the model used,that

Fig. 7

 7 Fig. 7 Variation of maximum of transversal velocity U 3max according to the nanoparticles volume fraction for N2 and N3 micropolar/non-micropolar nanofluid for Ra=10 5 and N=-0.2.

Figure 8

 8 Figure 8 shows the variations of average Nusselt number and Sherwood number with nanoparticles' volume fraction for micropolar/non-micropolar nanofluid stabilized with Lignin (N2) and sodium polycarboxylate (N3). Irrespective to the considred type of nanofluids, and are lower when the micropolar nanofluid model is under consideration, and are increased when the non-micropolar fluid model is under consideration irrespective of the values of nanoparticles volume fraction. It is noticed that for the two types of surfactants

Fig. 8 Fig. 9

 89 Fig. 8 Variation of

increased to - 1 ,Fig. 10

 110 Fig. 10 Influence of the buoyancy ratio N on isotherms, isoconcentrations and the projections of flow lines in the main plane z=0.5 for N2, K=1, Ra= 10 5 and

Fig. 11 5 Figure 12 Fig. 12

 1151212 Fig. 11 Variation of the average Nusselt and Sherwood numbers according the buoyancy fraction N for =0.055% and Ra=10 5 Figure 12 illustrates the variations of the horizontal and vertical velocity components in the plane (z=0.5) with respect to the Rayleigh number for micropolar CNT/water nanofluid stabilized with Lignin (N2) and sodium polycarboxylate (N3). The flow regime is intensified and the magnitude of each velocity component is increased with the increase in the Rayleigh number. Moreover, the difference between two nanofluids is much greater for Ra 10 5 .

Fig. 13

 13 Fig. 13 Variation of the average Nusselt and Sherwood numbers on the hot wall according to the Rayleigh number Ra and nanoparticles'svolume fraction for K=1 and N=-0.2

Fig. 14 Fig. 15 ,Fig. 15 :

 141515 Fig.14 Variation of maximum of transversal velocity U3max versus the Rayleigh number Ra and nanoparicles volume fraction for both N2 and N3 micropolar nanofluid for K=1 and N=-0.2.

Fig. 16 :Fig. 17 Fig. 18

 161718 Fig. 16: Time-dependent Nusselt and Sherwood numbers for N2 and N3 micropolar nanofluid for K=1, N=-0.2 and %

Figure 19

 19 Figure 19 depicts the variation of the average Nusselt and Sherwood numbers as functionof the vortex viscosity parameter K for two values of nanoparticles volume fraction. The average heat transfer rates are greater for non-micropolar nanofluid (K=0) when compared to micropolar nanofluid (K≠0). Figure 19 explains also that the values of and are decreased with an increase in K for both micropolar CNT/water nanofluid stabilized with Lignin (N2) and sodium polycarboxylate (N3). The physicsbehind the decrease in values of and can be explained as follows: an enhancing in the micro-constituents' concentration would lead to an amelioration in the vortex viscosity and the major part of the energy of the system is consumed for developing the gyrational velocities. As a result, the natural movement of molecules in the fluid was limitedand compensated by a decrease in heat and mass transfer rates.

Fig. 19 2 Figure20

 192 Fig. 19 Variation of average Nusselt and Sherwood numbers according the micropolar vortex parameter K for =0.055%, =0.557%and N=-0.2

Fig. 20

 20 Fig. 20 Variation of the maximum transverse velocity U 3max according the micropolar vortex parameter K, for =0.055%,=0.557%and N=-0.2

Fig. 21

 21 Fig. 21 Variation of the maximum of the components of microtation velocity H 1 max and H 2 max according to the micropolar vortex parameter K, for =0.055%, =0.557% , Ra=10 5 and N=-0.2



  Heat and mass transfer rates are lower for the micropolar nanofluid model when compared to the pure nanofluid model. Irrespective to the considered types of surfactant, the enhancement in the micropolar material parameter weakens both flow strength and three-dimensional character of the flow.  The flow strength and the three-dimensional effect of the flow are ameliorated when the nanoparticle volume concentration is less than the critical valueand then are deteriorated when it exceed this value for both two types of nanofluids. Both average Nusselt and Sherwood numbers increase withan increase in Rayleigh number. Employing a nanofluid stabilized with Lignin ameliorates the average Nusselt and Sherwood numbers more than that containing sodium polycarboxylate. Using nanofluid is better than pure water solution when nanoparticles volume concentration is less than a critical value. The micropolar model can describe the impacts of the microstructures on fluid motion. The microrotation of the nanoparticles seems to play a significant roleinto flow regime and in heat and mass transfer rates.

Table 1

 1 Thermophysical properties of nanofluid at T=20°C

	N2	N3

  Table 2Grid independence study (K=1, Ra=10 5 and φ=0.00055).

	Mesh size 31×31×31 41×41×41 51×51×51 61×61×61 71×71×71
		3.0866	3.1165	3.1168	3.1025	3.0998
		(0.9689%)	(0.0096%)		(0.45%)	(0.54%)
		3.4044	3.4456	3.4454	3.435	3.4247
		(1.305%)	(0.0017%)		(0.30%)	(0.60%)
	Then, the present simulation is validated with the three-dimensional results of the
	works performed by Sezai and Mohamad [49]. The numerical results presented in this study
	are limited to water-based solutions. The comparisons are presented in Table 3. It can be
	concluded that there is agood agreement between the value of	and	of the present work
	and the selected one for water based solution.
	Table 3Comparison with the results of Sezai and Mohamad [49] for Ra= 10 5 , Le=10, Pr =
			10
	N	Authors
	0	Present work		4.522	11.16
		Sezai and Mohammad [49]	4.532	11.046
		Percentage difference		0.22%	1.032%
	-0.2	Present work		4.483	10.757
		Sezai and Mohammad [49]	4.473	10.736
		Percentage difference		0.22%	1.20%
	-0.6	Present work		3.723	5.9572
		Sezai and Mohammad [49]	3.703	5.982
		Percentage difference		0.54%	0.41%
	-1.8	Present work		1.406	6.772
		Sezai and Mohammad [49]	1.396	6.782
		Percentage difference		0.71%	0.14%
	-2	Present work		1.367	7.204
		Sezai and Mohammad [49]	1.347	7.224
		Percentage difference		1.48%	0.27%

Acknowledgement:

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia for funding this work through the General Research Project under grant number (G.R.P-74-42).

The first author gratefully acknowledges the Tunisian Ministry of Higher Education and Scientific Research for financial support to her stay in LGCGM, France.


Madhukar Bhat

Jean-Marc Thiesse

Patrick Le Callet

ON ACCURACY OF OBJECTIVE METRICS FOR ASSESSMENT OF PERCEPTUAL PRE-PROCESSING FOR VIDEO CODING

Keywords: Perceptual pre-processing, Objective quality metrics, Paired comparison, critical pairs, perceptual performance

The objective assessment of encoding performance is a key aspect of video delivery optimization. Objective metrics typically do not address fully the different viewing distances and behavior of compression artifacts being subjected to perceptual changes in video. This poses a daunting task of optimizing compression for video delivery systems for specific viewing conditions and perceptual optimization. This paper introduces a perceptual pre-processing and then discusses accuracy of typically used objective metrics for judging performance of pre-processing for observers at different viewing distances. To this end, this paper reports an in-depth analysis to check if objective metrics can successfully match subjective results at critical pairs i.e. pre-processed and original video at same QP.

INTRODUCTION

Video coding in recent years have invested a considerable research in perceptual optimization of encoded video. Human perception of video consumptions are considered in video coding [START_REF] Chen | Perceptual video coding: Challenges and approaches[END_REF]. Application of human perception in video compression can be approached both within and outside encoding loop. In particular, video pre-processing is a conventional way to apply perceptual consideration outside video encoding loop.

Pre-processing models intends to remove as much information as possible within noticeable threshold from source video before encoding. Some of the earliest applications of pre-filtering were denoising filter [START_REF] Cheong | Adaptive spatio-temporal filtering for video denoising[END_REF] [3] to remove noise with edge preservation, which could reduce encoding performance. In [START_REF] Vanam | Perceptual pre-processing filter for user-adaptive coding and delivery of visual information[END_REF] advanced analysis lead to application of perceptual anisotropic filters based on contrast sensitivity map to consider Human Visual System (HVS) while removing information from video. Another perceptual modeling parameter considered was Just Noticeable Difference (JND) to control pre-filter proposed in [START_REF] Ding | Video preprocessing with jnd-based gaussian filtering of superpixels[END_REF].

When designing such perceptual pre-processing, having a reliable measure of performance of the algorithm is critical for calculating bit-rate savings at similar quality. Usually subjective tests are more suitable for quantifying improvements in perceptual optimization [START_REF] Hanhart | How to benchmark objective quality metrics from paired comparison data?[END_REF]. However, they are time consuming and costly. Objective quality metrics are therefore a relevant substitute for subjective test to reduce time, cost and impracticality of test design. But, quality metrics intended for performance evaluation of perceptual improvement should be verified by subjective data to reliably depend on them.

Evaluation of objective metrics for standard video compression quality measurement has been carried out in several studies [START_REF] Chikkerur | Objective video quality assessment methods: A classification, review, and performance comparison[END_REF] [START_REF] Seshadrinathan | Study of subjective and objective quality assessment of video[END_REF]. In these methods, classical performance evaluation frameworks like Pearson Linear Correlation Coefficient (PLCC) and Root-Mean-Square Error (RMSE) are used. In these frameworks, metrics are fitted by regression to map them to Mean Opinion Scores (MOS) which closely matches ITU-T recommendations [START_REF]Method for specifying accuracy and cross-calibration of video quality metrics (vqm)[END_REF] [START_REF]Subjective video quality assessment methods for multimedia applications[END_REF]. These methods use direct scaling methods for subjective test. But in case of pre-processing it is very important to judge stimuli whose visual difference are small. Indirect scaling methods like paired comparison (PC) which has higher discriminatory power is more suitable [START_REF] Hanhart | How to benchmark objective quality metrics from paired comparison data?[END_REF].

Reibman et al. [START_REF] Reibman | A probabilistic pairwise-preference predictor for image quality[END_REF] proposed a method to jointly test image quality estimators using paired comparison and many metrics. Hanhart et al. [START_REF] Hanhart | How to benchmark objective quality metrics from paired comparison data?[END_REF] proposed Receiver Operating Characteristic (ROC) based analysis to use indirect scaling data and Krasula et al. [START_REF] Krasula | On the accuracy of objective image and video quality models: New methodology for performance evaluation[END_REF] used direct scaling data for objective quality benchmarking. These frameworks test for finding accuracy of quality metrics in detecting significant difference between pairs of stimulus. They also allow finding accuracy for detection of better or worse stimulus in a specific pair.

This paper details the accuracy of commonly used objective metrics in assessment of perceptual pre-processing for video compression. The considered metrics include PSNR, MS-SSIM, VIF, VMAF [START_REF] Netflix | Toward a practical perceptual video quality metric[END_REF], PQR [START_REF] An | Understanding PQR, DMOS and PSNR measurements[END_REF] and HDR-VDP [START_REF] Mantiuk | Hdr-vdp-2: A calibrated visual metric for visibility and quality predictions in all luminance conditions[END_REF]. First, a perceptual pre-processing optimized for multiple viewing distances below JND threshold is used for treatment of video before encoding. Then both original and preprocessed videos are encoded using a professional HEVC encoder and are subjected to paired comparison test using square design [START_REF] Swets | Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers[END_REF]. Finally accuracy of objective metrics for judging critical pairs of pre-processed and original videos encoded at same QP are tested for two viewing distances using state of the art tools introduced in [START_REF] Hanhart | How to benchmark objective quality metrics from paired comparison data?[END_REF] and [START_REF] Krasula | On the accuracy of objective image and video quality models: New methodology for performance evaluation[END_REF]. This analysis provides details regarding accuracy of metrics for assessing RD-performance of pre-processing optimized for multiple distances. In addition an analysis is conducted for all possible pairs tested in subjective test to assess performance of metrics to evaluate RD-performance of general video compression.

This paper is organized as follows. Section 2 details the perceptual pre-processing algorithm used for the study. Section 3 explains the tools used for measuring accuracy of objective metrics. Experimental setup for paired comparison subjective test is given in section 4. Performance of objective metrics for pre-processing is discussed in section 5. Conclusions are drawn in section 6.

PERCEPTUAL PRE-PROCESSING ALGORITHM

Perceptual pre-processing used in this paper is built on accurate modeling of HVS for filtering within JND threshold. Relevant visual tools of HVS are involved, such as optical transfer function which is based on [START_REF] Deeley | A simple parametric model of the human ocular modulation transfer function[END_REF] and Contrast Sensitivity Function (CSF) which is based on [START_REF] Barten | Contrast sensitivity of the human eye and its effects on image quality[END_REF]. JND threshold is considered in applying masking effect on source video by controlling their shape. Both signal dependent (N CSF ) [START_REF] Watson | Model of visual contrast gain control and pattern masking[END_REF] and independent noises from CSF (N N mask ) are removed from video. Thanks to HVS base, pre-processing is naturally optimized for multiple viewing distances from the intended screening. Optimization for multiple viewing distance are conducted to study weather lack of modeling of distances in objective metrics affect their judgment at different intended viewing distances.

Two distances are used for analysis in this paper at 3H (height of the display) which is recommended minimum distance of the observer from full HD display and 4.5H which is the reference viewing distance for consumer. The optimization of masking effect for two distance changes because visual resolution of human eye can catch less errors from video moving away from the screen. Normalized CSF is applied to source video in multi-scale complex steerable pyramid [START_REF] Portilla | A parametric texture model based on joint statistics of complex wavelet coefficients[END_REF] domain.

Pre-processed band B pre (f, o) in f th scale and o th orientation band of steerable decomposition is obtained by applying N N mask and N CSF with gain controlling factor p on source band B src (f, o). It is expressed as,

B pre (f, o) = B src (f, o)   1 - 1 N 2p CSF + N 2 N mask   (1)
Visual display considered for optimizing pre-processing is standard LCD monitor at maximum brightness of 250cd/m2.

ANALYSIS OF ACCURACY OF OBJECTIVE QUALITY METRICS

Raw preference data from paired comparison test has to be processed as a first step before any analysis can be conducted. Paired comparison test used in this paper uses square design for choosing pairs within one video sequence. First raw subjective test data of each video sequence is processed to get relative score for each stimuli using Bradley-Terry method. This is followed by analyzing if the two pairs are significantly different or similar subjectively. If they are significantly different then from relative subjective score, better stimuli from the pair needs to be selected. Then, respective objective quality metrics data are gone through ROC analysis and classification errors. Performance difference between quality metrics can be found using accuracy measure. Analysis performed here are inspired by [START_REF] Hanhart | How to benchmark objective quality metrics from paired comparison data?[END_REF] and [START_REF] Krasula | On the accuracy of objective image and video quality models: New methodology for performance evaluation[END_REF].

Producing significantly different subjective pairs

First step in producing significantly different stimulus pairs in a video sequence is to process raw comparison data from paired comparison test. Raw preference scores are processed using Bradley-Terry model to obtain relative subjective scores (RS) of each stimuli with confidence index (CI) for a particular video sequence. It should be noted that one needs to be careful using these scores as relative scores between two different video sequences are meaning less. However, this remains relevant for this study since Bradley-Terry scores are only used to tell if the pairs are subjectively significantly different. From relative scores, two pairs S1 and S2 are significantly different if,

||RS(S1) -RS(S2)|| > CI (2)
If they are significantly different then the better stimuli is noted by comparing their scores.

Quality metric data processing

Objective quality for stimuli used for paired comparison can be obtained. Then for pairs used in subjective test difference in objective quality metric is taken as prediction of that metric for the pair. For each pair S1 and S2,

∆ OM (S1, S2) = score OM (S1) -score OM (S2) (3)
where, score OM (Si) are the quality prediction of a specific metric for stimuli pair. Difference of metrics obtained for each pair is compared with data from section 3.1 and then analyzed by methods described in the following sections.

Different v/s similar performance

In this analysis how well objective quality metrics detect significantly different and similar pairs compared to subjective model from section 3.1 is assessed. Usually ROC analysis is carried out to determine abilities of binary classifier [START_REF] Swets | Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers[END_REF].

Performance indicator in ROC curve can be obtained by Area Under Curve (AUC) [START_REF] Hanhart | How to benchmark objective quality metrics from paired comparison data?[END_REF]. Comparison between metrics can be obtained using their AUC values.

Better v/s worse performance

Another analysis useful in measuring accuracy of metrics is when pairs are different, whether a metric can also detect better/worse compared to subjective model from section 3.1. For this, AUC from ROC is calculated for better/worse analysis.

Classification Errors

Classification error for a stimulus pair(S1,S2) happens when a particular objective quality metric leads to different conclusion compared to subjective evaluation. There can be three types of errors. First one is False Tie error which occurs when objective metrics says S1 and S2 are identical but subjective models say that they are different. False Differentiation occurs when objective metrics classifies S1 and S2 as different when subjectively they are the same. False ranking which is most offensive error, which happens when objective metrics says S1(S2) is better than S2(S1) when it is the opposite in subjective test.

As explained ITU-T recommendation ITU-T J.149 [START_REF]Method for specifying accuracy and cross-calibration of video quality metrics (vqm)[END_REF], the percentage of Correct Decision (CD), False Tie (FT), False Differentiation (FD) and False Ranking (FR) are recorded from all possible distinct pairs as a function of metric value difference. In this paper classification errors are used to determine these four values for mean objective difference (∆OM mean ) for critical pairs.

EXPERIMENTAL SETUP

To measure the accuracy of objective quality metrics five 1080p video sequences are selected. Extensive paired comparison subjective tests and objective tests have been conducted to collect valid data for analysis of tools discussed in the last section. Performances of objective metrics is then calculated in the context of perceptual pre-processing for video compression using professional HEVC encoder. Subjective tests incorporated to evaluate the proposed framework follows ITU-T P.910 [START_REF]Subjective video quality assessment methods for multimedia applications[END_REF]. The subjective test protocols are explained in following paragraphs.

Selection of content and Stimuli

Video sequences used for calculating accuracy of perceptual pre-processing algorithm are five 1080p sequences at 50fps. Two videos, Basketballdrive and BQTerrace are selected from JCT-VC common test conditions [START_REF] Jctvc-L | Common test conditions and software reference configurations[END_REF]. Remaining three videos Crowdrun, Duckstakeoff and Oldtowncross are selected from SVT-HD test set [START_REF] Haglund | The SVT high definition multi format test set[END_REF] for diversity in spatial and temporal complexity and their wide range of use in video codec performance analysis.

Selection of stimuli for analysis is based on pre-processed and original video encoded at 4 different QP's. Similar quality level for comparison is selected based on expectation that at same QP both pre-processed and original videos behave in a similar way subjectively. It is verified through pre-analysis of All-Intra frames. Eventually, 4 QPs ranging from 20-42 for each sequence have been selected based on their RD-Curve.

Test environment

The selection of testing environment here is based on Recommendation ITU-T P.910 [START_REF]Subjective video quality assessment methods for multimedia applications[END_REF]. Two viewing distance corresponding to height of the display (H) at 3H and 4.5H are chosen. The luminance of the screen used for the test is 250cd/m2.

Paired comparison design

Paired comparison test conducted here uses squared design [START_REF] Dykstra | Rank analysis of incomplete block designs: A method of paired comparisons employing unequal repetitions on pairs[END_REF] with 9 Hypothetical Reference Circuits (HRC's) and 18 pairs to compare for each sequence. These come from one source and eight processed video encoded at different QP's from pre-processed and original videos. 30 naive observers participated in the test for each viewing distance.

RESULTS AND DISCUSSION

In this section, the application of analysis tools on perceptual pre-processing introduced in section 3 is reported for experimental setup explained in section 4. Subjective data from section 3.1 is compared with objective metrics data from section 3.2. First analysis of metrics for all possible pairs in video sequences to measure their accuracy is conducted. Then analysis of critical pairs for measuring accuracy of objective metrics for benchmarking pre-processing is carried out. Two viewing distances are separately analyzed to see if lack of modeling distances in objective metrics affect their judgment.

Overall pair Analysis

Table 1 depicts different/similar AUC and better/worse AUC for all the metrics used for analysis at both distances. Here performance of metrics are expectedly higher as most of the test pairs are with stimuli at different QP. Objective metrics often succeed to rank stimuli with large difference in subjective quality and algorithms without lot of perceptual considerations. Hence, they are popular in measuring performance of general video compression. It is also worth noting that at 4.5H AUC for different/similar analysis is a bit lower than that of 3H. It is because as one move away from screen it is difficult to differentiate pairs which are closer in quality. On the other hand with increasing distance (at 4.5H) if pairs are significantly different one can select better or worse more than at 3H. Since objective metrics do not model viewing distance, their performance decrease for different/similar analysis for other than optimized viewing distance.

Metrics

Critical pair analysis

Critical pairs are the pairs of pre-processed and original video encoded at same QP. Correct decision for these pairs from objective metrics is critical in assessment of pre-processing. Table 2 shows different/similar AUC and better/worse AUC for each metrics for both distances. Overall, the metrics have quite small AUC, except HDR-VDP which has substantially better scores compared to other metrics. This means that objective metrics are inefficient to judge quality of perceptual pre-processing. Since subjectively critical pairs are closer, objetive metrics often fail in judging them correctly. On the other hand HDR-VDP performs better than any metric at both distance with respectable AUC for both different/similar and better/worse analysis.

It can be seen from Table 2 that for different/similar judgment of stimuli viewing distance 4.5H is better than 3H for all metrics, which is reverse of what is found for overall pair analysis. This is due to the fact that pre-processing is optimized for two distances and observers found almost same number of pairs to be subjectively different/similar for both distance. But at 4.5H in better/worse analysis except for VMAF and VIF, other metrics perform better than at 3H. This is similar to the overall pair analysis.

Metrics

Different As explained in section 3.5 classification errors for the ∆OM mean of each metrics at critical pairs for both distance is given in table 3. HDR-VDP is significantly better in giving Correct Decision (CD) than other metrics at both distances. This is due to ∆OM mean of HDR-VDP, which is closest to the ∆OM value that maximizes correct decision compared to other metrics. At 3H except PSNR, all metrics can achieve very low False Ranking (FR). At 4.5H VMAF and PQR are prone to FR error. For VMAF it might be due to optimization done for decisions at 3H [START_REF] Netflix | Toward a practical perceptual video quality metric[END_REF]. Overall, False Differentiation (FD) score increases with distance for all metrics except for HDR-VDP. This is because HDR-VDP considers viewing distance in its calculation.

Lack of modeling of perceptual factors and viewing distance is apparent in most metrics except HDR-VDP as they perform differently with viewing distance and judge poorly the perceptual pre-processing for video coding. This poses a problem to reliably depend on objective metrics for judging RD-performance of perceptual pre-processing and its optimization for multiple viewing distances. Overall HDR-VDP is more accurate in judging performance of perceptual preprocessing.

Metrics

CONCLUSION

In this paper accuracy of objective quality metrics for measuring performance of perceptual pre-processing for video compression is tested. Even though objective metrics are fairly accurate for evaluating video compression algorithms in general, they perform very poorly for critical pair judgments. This study tends to suggest that objective metrics can be improved for accurately measuring RD-performance of perceptual optimizations such as pre-processing which involves tiny subjective differences. Further considerations in viewing distance and perceptual aspects are necessary for their reliability in judging perceptual algorithms. Even though computationally slow, HDR-VDP which takes into account viewing distance and perceptual modeling in judging two stimuli is the most suitable metric for assessing performance of perceptual pre-processing for video compression.

Table 1 .

 1 Different/Similar and Better/Worse AUC for metrics at both distances

		Different/Similar	Better/Worse
		3H	4.5H	3H	4.5H
	PSNR	0.9333 0.8808 0.9709 0.9905
	MS-SSIM 0.9491 0.8900 0.9772 0.991
	VIF	0.9539 0.8947 0.9722 0.995
	VMAF	0.9418 0.8958 0.9752 0.995
	PQR	0.9515 0.9074 0.9659 0.991
	HDR-VDP 0.9673 0.8938 0.9749 0.9904

Table 2 .

 2 Different/Similar and Better/Worse AUC for critical pairs

			/Similar	Better/Worse
		3H	4.5H	3H	4.5H
	PSNR	0.4633 0.5156 0.4171	0.5
	MS-SSIM	0.44	0.475	0.5257 0.625
	VIF	0.2667 0.2813 0.3829 0.375
	VMAF	0.4783 0.6031 0.4743 0.4681
	PQR	0.5133 0.6406 0.4629	0.5
	HDR-VDP 0.5967 0.7375 0.7489 0.8375

Table 3 .

 3 Classification errors for metrics

		CD	FT	FD	FR
		(%)	(%)	(%)	(%)
		3H 4.5H 3H 4.5H 3H 4.5H 3H 4.5H
	PSNR	55 60	15 10	25 30	5 0
	MS-SSIM 65 60	20 15	15 25	0 0
	VIF	57.5 60	20 15	22.5 25	0 0
	VMAF	62.5 65	20 10	17.5 25	0 5
	PQR	55 65	35 10	10 20	0 5
	HDR-VDP 75 75	10 15	15 10	0 0


Salma Benzarti
email: salma_benzarti@yahoo.fr

Hatem Mhiri

Hervé Bournot

Numerical simulation of baffled Circulating Fluidized Bed with Geldart B particles

Keywords: Circulating fluidized bed, Computational fluid dynamics, Hydrodynamic, Ring baffle effect

As most classical fluidization technologies, Circulating Fluidized Beds (CFB) are widely employed in chemical and physical operations. However, CFB Reactors still have some disadvantages such as the non-uniform solid particles distribution and the backflow of the solid particles near the wall, which deteriorate the system mixing, and lead to low system conversion/heat and mass transfer rate. To improve the CFB performance, we propose in the current work to study the effect of the ring baffle configuration on the fluidization system hydrodynamics using a multifluid Eulerian CFD model, incorporating the Kinetic Theory of Granular Flow. In this approach, two different types of ring baffles, circular and trapezoidal, were considered and the corresponding results were compared. The results revealed that the incorporation of ring baffles improved the system mixing and reduced the backflow near the wall. Nevertheless, the shape of baffles had a limited impact on the system hydrodynamics.

𝛩

Granular temperature m 2 s -2

Introduction

Circulating Fluidized Beds (CFBs) are a well-known device that has several significant advantages due to their effective contacting reactors' property and the continuous process they provide, coupled with a high throughput. They consequently have been widely used in industrial processes, such as chemical, petrochemical, pharmaceutical, metallurgical and energy-related industries [START_REF] Grace | Circulating Fluidized Beds[END_REF]. In spite of their widespread applications, CFBs still have some disadvantages, namely the non-uniform solid particles' distribution in both the radial and axial system directions as well as the back-fall of solid particles near the wall region, which deteriorate the system mixing and lead to low system conversion/heat and mass transfer rate [START_REF] Namkung | Gas backmixing in a circulating fluidized bed[END_REF][START_REF] Velden | Solids mixing in the riser of a circulating fluidized bed[END_REF].

One way to overcome the disadvantages of CFBs reactors is to install internal structures [START_REF] Jiang | Baffle effect on performance of catalytic circulating fluidized bed reactor[END_REF][START_REF] Zheng | Voidage redistribution by ring internals in fast fluidization[END_REF][START_REF] Zhu | Radial and axial voidage distributions in circulating fluidized bed with ring-type internals[END_REF][START_REF] Therdthianwong | Modeling and simulation of circulating fluidized bed reactor with catalytic ozone decomposition reaction[END_REF][START_REF] Samruamphianskun | Effect of ring baffle configurations in a circulating fluidized bed riser using CFD simulation and experimental design analysis[END_REF]. The main purpose of this solution is to scrape the down flowing solids away from the wall towards the center of the riser, leading to more uniform radial solid particles' distribution and intensify the gas-solids contact. There are several kinds of internal structures used in practice, such as ring baffles, perforated plates, tubes, inserted bodies, etc. Among all types of internal structures evaluated, ring baffles proved to highly enhance the radial mixing and reduce the back-mixing phenomenon with no effect from the overall system pressure drop. Jiang et al. [START_REF] Jiang | Baffle effect on performance of catalytic circulating fluidized bed reactor[END_REF],

investigated the effect of ring baffles on the performance of a catalytic Circulating Fluidized Bed Reactor (CFBR). They observed that the inclusion of ring baffles could improve the performance of a CFBR for the ozone decomposition reaction. Their experimental results

showed that in risers with ring baffles, the ozone concentration in the radial direction is much more uniform and the ozone conversion much higher at the lowest superficial gas velocity. Zhu et al. [START_REF] Zhu | Radial and axial voidage distributions in circulating fluidized bed with ring-type internals[END_REF], investigated experimentally the effect of internals ring types with various open area ratios on axial pressure distribution and gas-solids flow structure in a 7.6 cm-diameter and 3 m-height CFBR riser. They found that the ring baffles could reduce radial non-uniformity, evenly reorder the solid particles' radial distribution and formed a denser region above in contrast with a more dilute region below the ring baffle. Therdthianwong et al. [START_REF] Therdthianwong | Modeling and simulation of circulating fluidized bed reactor with catalytic ozone decomposition reaction[END_REF], conducted numerical studies in order to examine the hydrodynamics and ozone decomposition in CFBR with and without ring baffles. They found that the addition of baffles improve radial gas and solid particles' mixing and increase the ozone decomposition by approximately 5 to 12%.

Samruamphianskun et al. [START_REF] Samruamphianskun | Effect of ring baffle configurations in a circulating fluidized bed riser using CFD simulation and experimental design analysis[END_REF], used a factorial design analysis to investigate the effect of ring baffles design on the hydrodynamics of a CFBR riser. They found that the ring baffle opening area, the inter-baffle space and the interaction between these two terms have a significant effect on the solid particles' distribution and system mixing. More recently, Samruamphianskun et al. [START_REF] Samruamphianskun | Effect of operating parameters inside circulating fluidized bed reactor riser with ring baffles using CFD simulation and experimental design analysis[END_REF] investigated the effect of the operating parameters on the system hydrodynamics and mixing inside two CFBR risers with different ring baffle configurations using Computational Fluid Dynamics (CFD) simulations and a factorial experimental design analysis. The results showed that the operating parameters that had a significant effect on the distribution of solid particles were the inlet gas velocity and solid particle mass flux. They also found that the use of baffles in the mixing zone approximates the flow of the stuck profile, breaking the annulus and redirecting the catalyst particles to the center of the riser. As a result a high conversion and a significant reduction of the over cracking of the products was observed on the walls. The insertion of baffles in the feed region brings then greater uniformity in the distribution of particles in this region and decreases the speed of the core region, thus reducing the product sub-conversion.

As a continuity to above mentioned studies, we propose to explore in the present work the effect of the ring baffle configuration on the fluidization system hydrodynamics in a CFB filled with Geldart B particles using a multifluid Eulerian CFD model, incorporating the Kinetic Theory of Granular Flow. In this context, two different types of ring baffles, circular and trapezoidal, are considered and the corresponding results are compared.

Computational Fluid Dynamics simulation set up

System description

Our simulations are based upon the experimental work of Zaabout et al. [START_REF] Zaabout | Local solid particle behavior inside the upper zone of a circulating fluidized bed riser[END_REF]. The case system, as illustrated schematically in Fig. 1(a), is an ordinary CFB riser without ring baffles, with a cross-section of 0.2 × 0.2 m and a height of 2 m. The gas consists of air at ambient conditions while the solid particles are made of glass beads characterized by a density of 2400 kg/m3 and a sauter mean diameter of 120 µm (Geldart's Group B solid particles [START_REF] Kunii | Fluidization Engineering[END_REF]). The static bed height is 0.1 m and the system is simulated at a cold flow condition without any chemical reaction. The inlet gas are uniformly fed to the system at the bottom of the CFB riser with a superficial gas velocity of 1 m/s. The solid particles are fed from the one side inlet with a width of 0.05 m. the inlet solid particles' velocity was calculated from the solid mass flux of a 0.22 kg/m 2 s. The gas and solid particles exited the system from the top of the riser with a width of 0.1 m. The numerical model was validated in our previous work [START_REF] Benzarti | Numerical simulation of turbulent fluidized bed with Geldart B particles[END_REF]. In order to investigate the effect of the ring baffle configuration on the system hydrodynamics, two types of ring baffle configurations (circular and trapezoidal) were tested. The two modified riser geometries were displayed as a simplified schematic diagram in Fig. 1

Hydrodynamic model

To describe properly the 2D gas-solid flow, in the present study we propose to solve the governing equations of mass, momentum and granular energy for both the gas and solid phases by means of a transient Eulerian-Eulerian approach. In order to completely describe the governing equations, appropriate constitutive equation where specified to describe the physical properties in each phases. In the current work, we propose to use the equations based on the Kinetic Theory of Granular Flow (KTGF) developed by Gidaspow [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF] and available in the commercial software package Ansys Fluent. This theory's validity has been proven by many researchers [START_REF] Sun | Computation of circulating fluidized-bed riser flow for thefluidization VIII benchmark test[END_REF][START_REF] Neri | Riser hydrodynamics: simulation using kinetic theory[END_REF][START_REF] Huilin | Hydrodynamic simulations of gas-solid flow in a riser[END_REF][START_REF] Yunhau | Numerical prediction of combustion of carbon particle clusters in a circulating fluidized bed riser[END_REF][START_REF] Andreux | Hydrodynamic and solid residence time distribution in a circulating fluidized bed: Experimental and 3D computational study[END_REF] and was founded on the application used of the kinetic theory of dense gases to the particulate assemblies. This approach gives more perspicacity in terms of interactions between particles by assuming that binary collisions between hard spheres take

Air inlet

Solid inlet

Outlet place instantaneously. To describe the solid fluctuating kinetic energy, this model introduces one conservation equation called the granular temperature. The physical properties of the solid phase can therefore be obtained as a function of the restitution coefficient and the granular temperature. The momentum exchange between the two phases is accounted for by the drag coefficient, which has a significant effect on the prediction of the Eulerian-Eulerian model. In this study, the drag model of Gidaspow [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF] is used for this system, which has been shown to yield good predictions according to our previous work [START_REF] Benzarti | Numerical simulation of turbulent fluidized bed with Geldart B particles[END_REF]. The dispersed turbulent model is applied to describe the effects of the turbulent fluctuations of the velocities and the scalar quantities in the gas phase. This model is based upon the standard k-epsilon turbulence model with supplementary terms for the momentum exchange between the two phases. The calculation of the turbulence for the dispersed phase is achieved by application of the Tchen theory correlation [START_REF] Hinze | Turbulence[END_REF] into Fluent. These models have already been validated by comparison with the CFB experimental data of [START_REF] Zaabout | Local solid particle behavior inside the upper zone of a circulating fluidized bed riser[END_REF], and a perfect agreement between the computational and experimental data was already obtained [START_REF] Benzarti | Numerical simulation of turbulent fluidized bed with Geldart B particles[END_REF]. The governing equations with their constitutive equations are provided in Table 1.

Table 1 A summary of the governing equations and constitutive equations A.Governing equations (a) Mass conservation equations of gas and solids phases

𝜕(𝛼 𝜌 ) 𝜕𝑡 + ∇. 𝛼 𝜌 𝑢 ⃗ = 0 (1)
𝜕(𝛼 𝜌 ) 𝜕𝑡 + ∇. (𝛼 𝜌 𝑢 ⃗ ) = 0 (2)
𝛼 + 𝛼 = 1 (3)
(e) Equation of conservation of solids fluctuating energy in algebraic form

0 = -𝑃 𝐼 ̿ + 𝜏̿ : ∇u ⃗ -γ (8)

B.Constitutive equations

(a) Gas phase stress tensor

𝜏̿ = 𝛼 𝜉 - 2 3 𝜇 𝛻. 𝑢 ⃗ 𝐼 ̿ + 𝜇 𝛻𝑢 ⃗ + 𝛻𝑢 ⃗ (9)
(b) Solid phase stress tensor

𝜏̿ = -𝛼 𝜉 - 2 3 𝜇 (𝛻. 𝑢 ⃗ )𝐼 ̿ + 𝜇 (𝛻𝑢 ⃗ ) + (𝛻𝑢 ⃗ ) (10)
(c) Solid phase pressure

𝑃 = 𝛼 𝜌 𝛩 + 2𝑔 𝛼 𝜌 𝛩(1 + 𝑒 ) (11)
(d) Solids shear viscosity

𝜇 = 𝜇 , + 𝜇 , + 𝜇 , (12)
(e) Collisional viscosity [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF] 𝜇

, = 4 5 𝛼 𝜌 𝑑 𝑔 (1 + 𝑒 ) Θ 𝜋 (13)
(f) Kinetic viscosity [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF] 𝜇

, = 10 96 √Θπ 𝜌 𝑑 (1 + 𝑒 )𝛼 𝑔 1 + 4 5 𝑔 𝛼 (1 + 𝑒 ) (14)
(g) Kinetic viscosity [START_REF] Syamlal | Computer simulation of bubbles in a fluidized bed[END_REF] 𝜇

, = 𝛼 𝜌 𝑑 √Θπ 6(3 -𝑒 ) [1 + 2 5 𝑔 𝛼 (1 + 𝑒 )(3𝑒 -1)] (15)
(h) Frictional viscosity [START_REF] Schaeffer | Instability in the evolution equations describing incompres-sible granular flow[END_REF] 𝜇 , = 𝑃 sin 𝜙 2 𝐼

(i) Solids bulk viscosity [START_REF] Lun | Kinetic theories of granular flow: inelastic particles in coquette flow and slightly inelastic particles in a general flow field[END_REF]

ξ = 4 3 α 𝜌 𝑑 𝑔 (1 + 𝑒 ) Θ 𝜋 (17)
(j) Radial distribution function [START_REF] Lun | Kinetic theories of granular flow: inelastic particles in coquette flow and slightly inelastic particles in a general flow field[END_REF]

𝑔 = 1 - α α , / (18)
(k) Collisional energy dissipation [START_REF] Lun | Kinetic theories of granular flow: inelastic particles in coquette flow and slightly inelastic particles in a general flow field[END_REF]

𝛾 = 3(1 -𝑒 )𝛼 𝜌 𝑔 𝛩( 4 𝑑 𝛩 𝜋 ) (19)
(l) Gas-solid phase interphase exchange coefficient: Gidaspow drag model [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF] α g > 0.8

β = 3 4 C α (1 -α ) d ρ u ⃗ -u ⃗ α . α g ≤ 0.8 (20)
𝛽 = 150 (1 -𝛼 ) 𝛼 𝜇 (𝑑 ) -1.75(1 -𝛼 ) 𝜌 𝑑 𝑢 ⃗ -𝑢 ⃗ (21)

Initial and boundary conditions

For both the gas and solid particles' entries, the velocity inlet boundary condition was used while for the outlet, the pressure outlet boundary condition was applied. The system pressure was entered as an atmospheric pressure. For the solid particles, the initial solid inventory in the riser was set using available experimental data [START_REF] Zaabout | Local solid particle behavior inside the upper zone of a circulating fluidized bed riser[END_REF]. At the wall, the boundary condition of Johnson and Jackson [START_REF] Johnson | Frictional-collisional equations of motion for participate flows and their application to chutes[END_REF] was applied which assumes no slip for the gas and partial slip for the solid phase. This condition has been successfully applied to KTGF modeling by Sinclair and Jackson [START_REF] Sinclair | Gas-particle flow in a vertical pipe with particle-particle interaction[END_REF]. Physical properties and simulation parameters are listed in Table 2.

Results and discussion

In the current study, the system hydrodynamics were described in terms of the distribution In addition to the solid volume fraction, the pressure drop is a further parameter that requires full attention when adding ring baffles into the riser since the flow interruption from the ring baffles may induce the system pressure to drop or the energy requirement to increase.

The computed time-averaged system pressure drops along the height of non-modified and modified CFB risers are shown in Fig. 4. In absence of ring baffles, the system pressure drop profile for the case without ring baffles has a smooth exponential shape which divided into two distinct zones: the acceleration zone and the established zone. At the bottom of the bed, the entering particles are accelerated by gas flow. Due to a relatively higher solids' holdup and the particle acceleration, this region displays a high-system pressure drop. This part of the riser is called the acceleration zone. Beyond this acceleration region, the system pressure drop does not significantly change. This implies that at the upper part of the riser both the particle velocity and the solid holdup become constant, this is the established zone. The presence of the baffles in the fluidization column affects significantly the axial distribution of the pressure drop by the introduction of pressure drop peaks at the location of the ring baffles and tends to decrease at other locations which is mainly due to the high particle retention and the particles' accelerations effects around the rings, as explained by Bu and Zhu [START_REF] Bu | Influence of ring-type internals on axial pressure distribution in circulating fluidized bed[END_REF]. This explanation assumes that the particles accumulated in the baffle region absorb more kinetic energy to climb into the column, which results in an increased pressure drop in this area. The solids acceleration zone is inherent to the circulation fluidized beds. However, it is undesirable for many reactions because of the increased back-mixing in this relatively dense region. The addition of ring baffles seems to sensibly reduce the length of this acceleration section. In fact, this action considerably reduced the length of this zone from 1.4 m for the reference case (case 1) to 1 m for the two configurations with baffles. The installation of the baffles improves then the quality of axial mixing within the fluidization column, probably due to the narrower path way created by the ring baffles, which leads to a higher gas velocity and then assists to the acceleration of solids. On the other hand, it should be noted that the implementation of ring baffles is pronounced only at the acceleration section, whereas, in the top developed section, the pressure appears to be similar for all profiles. We finally note that the shape of the ring baffles has a limited impact on the distribution of the system pressure drop (similar plots and close peak values).

The system mixing can also be idescribed by means of the axial and radial solid particle and gas velocity distributions. The axial distributions of the time-averaged axial solid particle and gas velocities of the CFB riser with different ring baffle configuration are displayed in Fig. 5 where positive value means the upward movement while the negative values mean a downward movement. The introduction of ring baffles has a significant effect, expressed through a higher level of fluctuation along the axial distribution of the different plotted velocities. In fact, when the solid particles pass through the baffle zone, they change direction and promoting fluctuations along the axial velocity profiles. The flow of the two phases becomes consequently much more turbulent, contributing then to the increase of the intensity of the axial mixing.

The axial distribution of the time-averaged radial velocities of both solid particles gas within the CFB riser under different ring baffle configurations are plotted in Fig. 6, where positive values represent a left to right particle movement and negative values a right to left movement. For all three riser geometries, the radial gas and solid particle velocities are lower than the axial ones, since the axial direction is the main direction of the system flow. The addition of the ring baffles increases the solid particles' movement, through higher positive and negative radial solid particle and gas velocities. In fact, when the solid particles reach the ring baffles positions, they are induced into the center region, a radial movement resulting in a sign change in both radial velocities along the CFB riser height. The effect of the ring baffles introduction over the radial velocities is further emphasized in the bottom of the riser. In fact, for the two modified configurations, we can clearly observe the high positive and negative radial solid particle and gas velocities. These variations are due to the combination of an increase in the gas velocity in the riser center due to the ring baffles and the movement of solid particle from the inlet to the opposite wall. Due to this secondary solids flow, the particles circulate though the walls and are dragged from one side to the other. Therefore, cases 2 and 3 had a low opportunity to form particle clusters near the wall region in the bottom zone of the riser, promoting as a result the radial gas-solid particle mixing. As we rise in the column, the fluctuation decrease sensibly and the profiles converge towards the basic configuration profile with small discrepancies in the values reached. This suggests that the improvement of the radial mixture by the installation of baffles is more pronounced in the lower zone of the column characterized by a strong retention of solid particles.

The radial distribution of the time-averaged axial solid particles' velocity within the CFB riser with and without ring baffles at two axial positions between the rings (H=0.5 m and H=1.3 m) are illustrated in Fig. 7. The overall observation of these plots reveals a central region characterized by an upward movement of the solid particles (positive velocities) and an annular region characterized by a downward movement for all configurations. Cases 2 and 3 o have the lowest negative axial solid particles' velocities due to having the lowest level of solid particles falling downwards, near the wall region. The ring baffles block consequently the solid particles fall down and force them to move to the center region that likely leads to a lower solid back mixing than the reference case (case 1). We can also see from these plots that for the cases 2 and 3, the thickness of the central region (0.01<X<0. [START_REF] Hinze | Turbulence[END_REF]) is extended reflecting a better quality of the mixing in this region. We can also note in this figure that for the two modified configurations, the profiles of the time-averaged axial solid particle velocity are almost coincide with slight difference in the values reached. This suggests that the shape of the baffles has limited impact on the radial distribution of the axial solid particles' velocity.

The radial distributions of the time-averaged radial solid particles' velocities in the CFB risers with and without ring baffles for two axial positions between the rings (H=0.5 m and H=1.3 m) are displayed in Fig. 8. The plots highlight the preponderance of the axial flow, since the velocity values of the solid particles in the axial direction (Fig. 7) are much greater than those in the radial direction. We can also see from these plots that the modification made on the CFB riser has a significant effect on the solid particles' flow in the radial direction. Indeed, the cases 2 and 3 have more fluctuating profiles than the case without ring baffles as indicated by the numerically larger positive and negative values of the radial solid particles' velocity at the right and left sides of the system. The increase of the radial velocity is more pronounced in the transition region between the core and the annular region that reached up to 0.4 m/s at H=0.5 m , which reflects the existence of a privileged area for the transfer of mass from the core to the annular region. Indeed, the brusque enlargement of cross-sectional area of the riser caused by the shape of the baffles contributes to the formation of recirculation zones at the corners and therefore to the entrainment of the two phases towards the walls. This flow pattern induces a significant increase of the velocity in the transition zone between the core and the annular and thus the improvement of the mixing quality in the radial direction. This statement is comforted by Fig. 9, where the streamlines of the gas phase for the two modified configurations reveal the formation of the vortex (recirculation zone) structures developed just above the baffles. From Fig. 8, we can also observe that the shape of the baffles affects the radial distribution of the radial velocity. In fact, for case 3, the mean radial solid particle velocities are higher than those of the case 2. This suggests that the case 3 has a low possibility to form clusters and therefore a great possibility, to improve the gas-solids mixture quality in the radial direction.

Conclusion

An Eulerian-Eulerian CFD model incorporating the Kinetic Theory of Granular Flow (KTGF) was applied by means of the commercial CFD package Ansys Fluent in order to explore the effect of ring baffle configuration on the fluidization system hydrodynamics in a CFB riser filled with Geldart B particles. In this approach, two different types of ring baffles, circular and trapezoidal, were considered. As can be seen from the simulation results, the insertion of ring baffles into a CFB riser has a significant effect on the flow patterns. The ring baffles improved the system mixing in both radial and axial direction and reduced the backflow near the wall, which allowed a higher benefit for heat and mass transfer in this CFB riser system. It was also found that the shape of the ring baffles had a limited impact on the system hydrodynamics.

(e) Collisional viscosity [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF]

(l) Gas-solid phase interphase exchange coefficient: Gidaspow drag model [START_REF] Gidaspow | Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[END_REF] α g > 0.8

β = 3 4 C α (1 -α ) d ρ u ⃗ -u ⃗ α .
α g ≤ 0.8

Highlights

 The circulating fluidized bed with ring baffles was investigated.  Eulerian-Eulerian approach with Gidaspow gas-solid drag model and standard k-e model was performed  Two ring baffle configurations were investigated.  Time-averaged results relative to circulating fluidized beds in presence and in absence of ring baffles were compared.  The incorporation of ring baffles improved the system mixing and reduced the backflow near the wall *Highlights (for review)

NomenclatureC

  2ε ,C 1ε Turbulence model Coefficients -

3 Fig. 1 .

 31 Fig. 1. Schema of the different CFBR tested geometries: (a) without baffles (b) with circular ring

( b )

 b Momentum conservation equations of gas and solids phases 𝜕(𝛼 𝜌 𝑢 ⃗ ) 𝜕𝑡 + ∇. 𝛼 𝜌 𝑢 ⃗ 𝑢 ⃗ = ∇. 𝜏̿ -𝛼 ∇𝑃 -𝛽 𝑢 ⃗ -𝑢 ⃗ + 𝛼 𝜌 𝑔 (4) 𝜕(𝛼 𝜌 𝑢 ⃗ ) 𝜕𝑡 + 𝛻. (𝛼 𝜌 𝑢 ⃗ 𝑢 ⃗ ) = 𝛻. (𝜏̿ ) -𝛼 𝛻𝑃 -𝛻𝑃 -𝛽 𝑢 ⃗ -𝑢 ⃗ + 𝛼 𝜌 𝑔 ((𝛼 𝜌 𝑢 ⃗ 𝛩) = -𝑃 𝐼 ̿ + 𝜏̿ : 𝛻𝑢 ⃗ -𝛻. 𝑞 -𝛾 -𝐽

  of the solid volume fraction and the radial and axial velocities of the solid particles. The contours of the instantaneous solid concentration in the circulating fluidized bed at t=30 s for the non-modified and modified risers are given in Fig.2. Two coexisting regions, characteristic of the turbulent fluidized bed (a bottom dense region and a top dilute region), are observed for all tested cases. The addition of ring baffles into the circulating fluidized bed has a significant effect on the distribution of the two phases. It makes, the solid volume fraction in both modified CFB risers evidently more homogeneous along the CFB riser column then in the reference case (case 1). In both modified risers, cases, most of the solid particles flew upwards at the center region and only few solid particles fell downwards near the wall region. This is due to the presence of the ring baffles that improves the breaking of the clusters near the wall region and pushes the solid particles towards the center of the flow. Plots on Fig.3to Fig.8are time-averaged results at the quasi-state condition, over 10 to 30 seconds of simulation time.For instance, Fig.3present the time-averaged solid volume fractions along the height of CFB riser under different ring baffle configurations. The Time-averaged solid volume fraction for the two modified configurations is much lower than that of the reference configuration, thus justifying the significant effect of the geometrical structure on the particles' flow. Fig.3also shows a uniform time-averaged solid volume fraction over a longer distance (1.2-2 m) in the riser with comparison to the reference configuration (1.6-2 m), indicating a better axial dispersion of the solids. We can also observe from these plots that the cross-sectional mean solid holdup for case 2 and case 3 are confused with the existence of a moderate difference in the values reached. This observation suggests that the shape of the ring baffles has a limited impact on the distribution of the particles in the center of the column.

a) Case 1 b) Case 2 c) Case 3 Fig. 2 .Fig. 3 . 2 Fig. 4 .Fig. 5 . 6 Fig. 6 . 2 Fig. 7 .Fig. 8 .Fig. 9 . 3 Fig. 1 .Fig. 2 .Figure 2 Fig. 3 .Figure 3 Fig. 4 .Figure 4 Fig. 5 .Figure 5 Fig. 6 .Figure 6 Fig. 7 .Figure 7 Fig. 8 .Figure 8 Fig. 9 .Figure 9 1 A

 13232456627893122334455667788991 Fig. 2. The contours of instantaneous solid volume fraction at 30 s in CFB riser: (a) without baffles

  𝜌 𝑢 ⃗ -𝑢 ⃗ 𝑑 𝜇[START_REF] Johnson | Frictional-collisional equations of motion for participate flows and their application to chutes[END_REF]

Table 2 .

 2 Modeling parameters

	Description	Value
	Bed height H	2 m
	Bed width	0.2 m
	Static bed height 𝐻	0.1 m
	Gas density 	1.2 Kg/m 3
	Particle density s	2400 Kg/m 3
	Particle diameter ds	120 µm
	Initial solid volume fraction 	0.6
	Inlet gas velocity 𝑈	1 m/s
	Solid flux 𝐺	0.22 kg/m 2 s
	Angle of internal friction	30°
	Restitution coefficient 𝑒	0.9
	Specularity coefficient φ	1
	Maximum particle packing limit	0.64
	Time step	10 -4s

Table 1

 1

		𝜇 , =	4 5	𝛼 𝜌 𝑑 𝑔 (1 + 𝑒 )	Θ 𝜋	(13)
	(f) Kinetic viscosity [13]
	𝜇 , =	10 96	√Θπ	𝜌 𝑑 (1 + 𝑒 )𝛼 𝑔	1 +	4 5	𝑔 𝛼 (1 + 𝑒 )	(14)
	(g) Kinetic viscosity [20]
	𝜇 , =	𝛼 𝜌 𝑑 √Θπ 6(3 -𝑒 )	[1 +	2 5	𝑔 𝛼 (1 + 𝑒 )(3𝑒 -1)]	(15)
	(h) Frictional viscosity [21]
					𝜇 , =	𝑃 sin 𝜙 2 𝐼	(16)
	(i) Solids bulk viscosity [22]

Table 2 .

 2 Modeling parameters

	Description	Value
	Bed height H	2 m
	Bed width	0.2 m
	Static bed height 𝐻	0.1 m
	Gas density 	1.2 Kg/m 3
	Particle density s	2400 Kg/m 3
	Particle diameter ds	120 µm
	Initial solid volume fraction 	0.6
	Inlet gas velocity 𝑈	1 m/s
	Solid flux 𝐺	0.22 kg/m 2 s
	Angle of internal friction	30°
	Restitution coefficient 𝑒	0.9
	Specularity coefficient φ	1
	Maximum particle packing limit	0.64
	Time step	10 -4s

Table 2

 2

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.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: × *Declaration of Interest Statement