CFD Study of the Fluid Viscosity Variation and Effect on the Flow in a Stirred Tank Achouri Ryma, Hatem Dhaouadi, Hatem Mhiri, Philippe Bournot

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1 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng CFD Study of the Flud Vscosty Varaton and Effect on the Flow n a Strred Tank Achour Ryma, Hatem Dhaouad, Hatem Mhr, Phlppe Bournot Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ Abstract Strred tanks are wdely used n all ndustral sectors. The need for further studes of the mxng operaton and ts dfferent aspects comes from the dversty of agtaton tools and mplemented geometres n addton to the specfc characterstcs of each applcaton. Vscous fluds are often encountered n ndustry and they represent the maorty of treated cases, as n the polymer sector, food processng, pharmaceutcals and cosmetcs. That's why n ths paper, we wll present a three-dmensonal numercal study usng the software Fluent, to study the effect of varyng the flud vscosty n a strred tank wth a Rushton turbne. Ths vscosty varaton was performed by addng carboxymethylcellulose (CMC) to the flud (water) n the vessel. In ths work, we studed frst the flow generated n the tank wth a Rushton turbne. Second, we studed the effect of the flud vscosty varaton on the thermodynamc quanttes defnng the flow. For ths, three vscostes (0.9% CMC, 1.1% CMC and 1.7% CMC) were consdered. F Keywords CFD, CMC, Mxng, Vscosty, Rushton turbne. I. INTRODUCTION ROM the coffee cup to the gant cement slo, a mxng scence was developed to study all nteractons that can take place nsde t: heat transfer, mass transfer, the mxer power, the vscosty and shear... Today, ndustres such as pharmaceutcals, food ndustry or water treatment have become aware of the need for a serous consderaton of mxng as the mxture st for a long tme on emprcal correlatons. Our research was made to gve a numercal study of a strred tank wth a Rushton turbne, and to try to mprove the mxng performances when changng the flud vscosty. Ths mprovement s made by changng the turbne poston nto the tank, and to study the hydrodynamc parameters of each poston. Some research focused on the geometrcal parameter of the tank lke [1] and the applcatons of CFD method n a large scale tank [2]. The case of tanks wth and wthout nternals obstructons was also studed [3], usng n hs work experments and CFD Models. Many CFD approaches for studyng and predctng the flow feld n a strred tank were studed: A comparson was made between several CFD approaches [4] for predctng the flow feld n a mxed reactor. Ryma Achour and Hatem Mhr are wth the UTTPI, Natonal Engneerng School of Monastr, Tunsa (phone: ; fax: (+216) ; e-mal: ryma_achour@yahoo.fr; hatem.mhr@enm.rnu.tn). Hatem Dhaouad s wth Unversty of Monastr, Scences Unversty, UR1204- Appled Chemstry Envronment (e-mal: hatem.dhaouad@ fsm.rnu.tn). Phlppe Bournot s wth IUSTI, UMR CNRS 6595, 5 rue Enrco Ferm, Technopole de Château-Gombert, 1303 Marselle, France (e-mal: bournot@unvmed.fr). Some used the code Fluent [5] to smulate the lamnar and turbulent flow generated by a Rushton turbne n a baffled tank. They proposed and appled numercal smulaton by Snapshot (method of the black box) and has valdated hs results by hs prevous expermental work. The sldng mesh was assessed [6] by CFD and measured by LDA the flow present n a vessel wth four baffles and agtated by a Rushton turbne. A study [7] focused on the energy consumpton of the flow n a strred tank, for dfferent types of agtaton mobles. A comparson of the parameters of the flow (speed, turbulent knetc energy, energy dsspaton rate ), for the same energy, was conducted to characterze the flow generated by strrers. The CFD predctons have been valdated by LDA measurements. The avalable technques for the study of flow nduced by dfferent types of agtators, such as classcal technques of measurng velocty by the pressure dfference, the tube of Ptot and the hot wre, or even new as LDV, fluorescent technques nduced by laser and the PIV, were revewed and dscussed [8]. LES model was adapted [9] and the sldng mesh model to study a tank mxed by a Rushton turbne equpped wth sx blades. The results were assessed based on expermental studes [10] and showed that the LES model s a relable tool to study the tme-varyng behavor of turbulent flow n agtated tanks. Other researchers [11] were nterested by the Rushton turbne submergence effect on the velocty feld. The results showed that for a small clearance, the flud flow s changng from a radal (at two loops) typcal feld to an axal feld smlar to that generated by a propeller. They found that ths profle leads to an ncrease of the axal flow and a reducton n the tme of mxture for the same power number. Other ones [12] have compared three methods for the smulaton of mxng n a baffled tank. Predctons of CFD were presented for the Rushton turbnes and propeller and results were compared wth the experence and lterature. A dfferent study [13] was about the dstrbuton of the turbulent energy dsspaton rate ε n a tank agtated by a Rushton turbne by a CFD study based on sldng mesh technque. They showed that the estmatons of ε obtaned from the macro scales of turbulence may overestmate the amount of energy dsspated n the volume swept by the turbne, whle LDA studes ndcate that a good amount of energy s dsspated around the walls and baffles. Concernng the studes on the effect of vscosty, some studes were expermental [14] usng the LDV measurement to calculate the hydraulc effcency and structure of turbulence for three agtators: Rushton turbne agtators and two axal flow agtators: a Mxel TT and Lghtnn A310. Mxel TT had the best performance for a Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

2 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ vscous lqud (soluton 1% CMC). All three had a relatvely low effcency. The authors found that the energy was manly dsspated n the stream swept by the turbne and the man crculaton loop. Other researchers added the numercal method [15] and have seen that the numercal smulaton of vscous fluds n a strred tank s nsuffcent and further development s requred. They made the numercal smulaton by CFD and PIV expermental study to examne the flow feld of a vscous flud n a tank agtated by a Rushton turbne wth four blades. The studed soluton s the mxture of water wth dfferent concentratons of glycerol. As a result, the mean velocty, turbulent energy, the pumpng of fluds and the flow feld change wth the flud vscosty. Ths numercal study was performed wth the commercal code CFX4.4 and a sldng mesh. A recent study [16] attempted to generate the data flow of non-newtonan fluds by conductng tracer experments n a tank strred by an anchor-type strrer. The fluds studed are water, castor ol, methyl esters of castor ol, carboxymethylcellulose (soluton 0.5 and 1% concentraton), suspenson of pulp (0.5% and 2 % concentraton) and the suspenson of starch (2% and 4% concentraton) wth the presence or absence of aeraton. The authors found an ncrease n the effcency of mxng wth ncreasng rotatonal speed. The numercal flud mechancs (CFD) s a robust tool n the predcton of flow n strred tanks. The commercal code "Fluent" wll be the CFD tool of ths work whch wll focus on the modelng and on the numercal smulaton of a strred reactor wth a Rushton turbne, ncludng the flud vscosty effect n such a system. Ths artcle presents our recent efforts for a better understandng of the turbulent flow n a strred tank wth a Rushton turbne, and for the vsualzaton of the flud vscosty effect. For the best descrpton of the flud flow, we used the Euler-Euler multphase model and the turbulence model k-ε standard avalable n Fluent to descrbe the flud flow n ths type of turbne and also to study ts performance, n order to optmze the strrng process and to mprove the hydrodynamc parameters governng the flud flow. A. Studed Feld II. CFD MODELING The studed feld s a flat bottomed and an unbaffled tank, havng a Rushton turbne wth 6 blades as a mxer. The dameter of the tank, T, s equal to 0.36m, heght H s equal to fve quarts of T (H = 5/4T = 0.45m), and the water level n the tank s h equal to three quarts of T (h = 3/4T = 0.27m). The clearance (dstance between the bottom of the tank and the turbne) of our turbne s C= 0.2m. The geometry of our feld s represented n Fg. 1, and the dmensons of the Rushton turbne are resumed n Table I. TABLE I DIMENSIONS OF THE RUSHTON TURBINE Desgnaton Varable Value (m) D Impeller Dameter d Turbne's dsk dameter E Thckness of the turbne's dsk L p Blade Length l p Blade wdth 0.02 e p Blade thckness Fg. 1 Dmensons of the studed feld B. Mesh and Boundary Condtons The mesh creaton s a delcate stage. Mesh qualty s defned by the refnement of the mesh. In fact a farly tght mesh leads to more accurate results whle t ncreases sgnfcantly the number of meshes resultng n a longer computaton tme. It s necessary to defne an area surroundng the turbne rotor (MRF: Movng Reference Frame) and a stator area. For an optmal mesh we worked n two steps: The frst step s to dvde the area nto three parts. The mddle area, whch contans the Rushton type turbne, has a tghter mesh than the two others. It ncludes the MRF, wth a tetrahedral mesh and the free surface wth a mesh sze even more refned for a better accuracy. The second step s based on the need to reduce the total number of cells and ncrease the accuracy n the whole area. So we only consdered the sxth confguraton, takng nto account the feld symmetry and the unform hexahedral mesh tghter than the prevous full confguraton. Therefore, we adopted the grd of one sxth of the confguraton, after many grd ndependence studes. The followng Fg. 2 shows the meshed doman for both methods, and the boundary condtons are showed n Table II. Area Tank Walls Turbne (Mxer+ Shaft) Area around the Mxer Top of the Tank TABLE II BOUNDARY CONDITIONS Boundary Condtons Wall Wall Movng Reference Frame (N=250 rpm) Pressure Outlet (P*=P atm) Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

3 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng 2. Conservaton Equatons: The governng equatons for an uncompressble flud can be wrtten as: ρ + ( ρu ) = 0 (1) t Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ C. Governng Equatons Fg. 2 Mesh of the studed feld In order to study the flow n our confguraton and the varous thermodynamc quanttes characterzng t, we used a smulaton model and the Euler-Euler multphase. Unlke other models, the Euler model solves equatons of transport and contnuty for each phase. The couplng s then acheved through pressure and heat transfer coeffcents between phases. In our case, a three-dmensonal smulaton was performed for an ar-water multphase system. The model MRF (Movng Reference Frame) was used to smulate the dfferent nteractons between the rotatng turbne and the tank and ts walls. The turbulence generated by the turbne s modeled usng the turbulence model k-ε standard. Ths model s sutable for flows wth fully developed turbulence (hgh Reynolds number). The detals of the turbulence model, as well as those of the MRF model, and the equatons governng these models wll be dscussed. 1. Expermental Measurement of Flud Vscosty Measurng the vscosty of a flud s a crtcal step n the smulaton because t depends on the nature of the chosen flud and the tool used to take measurements. In ths secton, we present our used flud and the vscosty measurements. In our study, we have n our tank 27 lters of water. We wll vary the vscosty by addng 250g of CMC n the water for the frst case, 300g of CMC n the second case and 450g for the thrd case. We wll have three solutons wth a percentage by mass, respectvely 0.9% CMC, 1.1% CMC and 1.7% CMC. The vscosty of non-newtonan fluds s measured usng a rheometer. We fnally obtaned the vscosty, the densty and the Reynolds number of every studed flud, whch are summarzed n Table III. TABLE III CHARACTERISTICS OF STUDIED FLUIDS CMC Concentraton (%) µ (CPS) (1 Cps = 10-3 Pa.s) ρ (kg/m3) Re t ( ρu ) + ( ρu u ) = ( ρu ) + ' ' ( ρuu ) P u u µ + + x x (2) where the velocty components are dvded nto the mean u ' and the fluctuatng u veloctes. These two components are related to each other by the followng equaton: u = u + u Equatons (1) and (2) are called Reynolds-Averaged Naver- Stokes (RANS) equatons. The Reynolds stress term R = ρu u represents the effects of turbulence and must be ' ' modeled to fully characterze (2). 3. MRF Model: The computatonal doman for the CFD problem was defned wth respect to the rotatng frame so that an arbtrary pont n the CFD doman s located by a poston vector r from the orgn of the rotatng frame. The flud veloctes can be transformed from the statonary frame to the rotatng frame usng the followng relaton: where v u r ' v r u r (3) = (4) = Ω r In these equatons u r s the whrl velocty (the velocty due to the movng frame), v r s the relatve velocty (velocty vewed from the rotatng frame), and v s the absolute velocty (velocty vewed from the statonary frame). When the equatons of moton are solved n the rotatng reference frame, the acceleraton of the flud s augmented by addtonal terms that appear n the momentum equatons. Moreover, the equatons can be formulated n two dfferent ways: Expressng the momentum equatons usng the relatve veloctes as dependent varables (known as the relatve velocty formulaton), or expressng the momentum equatons usng the absolute veloctes as dependent varables n the momentum equatons (known as the absolute velocty formulaton). (5) Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

4 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng 4. The Standard k ε Model: The standard k- ε model s a sem-emprcal model based on model transport equatons for the turbulence knetc energy (k) and ts dsspaton rate (ε). The model transport equaton for k s derved from the exact equaton, whle the model transport equaton for ε was obtaned usng physcal reasonng and bears lttle resemblance to ts mathematcally exact counterpart. The turbulence knetc energy, k, and ts rate of dsspaton, ε, are obtaned from the followng transport equatons: Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ and ( ρk) ( ρku ) + = t + G ( ρε + Y b M ε C1 ε ( Gk + C3εGb ) C2 k ) µ t k µ + + G σ k ( ρε ) ( ρεu) µ t ε + = µ + t x x + σ ε ε 2 ε ρ k In these equatons, G k represents the generaton of turbulence knetc energy due to the mean velocty gradents, G b s the generaton of turbulence knetc energy due to buoyancy, Y M represents the contrbuton of the fluctuatng dlataton n compressble turbulence to the overall dsspaton rate, C 1ε, C 2ε, and C 3ε are constants, σ k and σ ε are the turbulent Prandtl numbers for k and ε, respectvely, and S k and S ε are user-defned source terms. III. NUMERICAL RESULTS AND DISCUSSIONS To study the vscosty effect n a strred tank wth a Rushton turbne, we wll compare the numercal results from the calculaton code Fluent of four solutons of dfferent vscostes. When usng only water, we are n a full turbulent regme, whle for CMC solutons we are n transent regme. In ths secton we wll study the dfferent aspects and phenomena n a strred tank wth a Rushton turbne equpped wth sx blades, mmersed at 7cm of the vessel free surface. Smulatons are based on the assumptons chosen prevously, wth dfferent vscostes of the flud adopted. As a frst step of ths work, we focused on the volume fracton contours for the four studed cases, shown n Fg. 3. k (6) (7) Fg. 3 Contours of the dstrbuton of the volume fracton of phases n water contanng a) 0% CMC, b) 0.9% CMC, c) 1.1% CMC and d) 1.7% CMC We notce that the mxng phenomenon s more effcent for the smaller vscosty,.e. the water case, wth a less pronounced vortex. Ths s due to the resstance forces whch ncrease wth the ncrease of the flud vscosty, so the mxng of ar nto the flud s easer wth a less vscous flud. For the same reason, we have a stagnant area below the turbne whch ncrease wth vscosty, and ths can also be explaned by the turbne poston whch suts better for surface aeraton, and provdes a good mxng but not a perfect one. To better understand why the volume fracton contours are the way they are, we are now nterested by the mean velocty vectors of varous CMC concentratons n the md plane wth the rotatonal speed of 250 rpm shown n Fg. 4. Fg. 4 Dstrbuton of velocty vectors (m / s) for water contanng a) 0% CMC, b) 0.9% CMC, c) 1.1% CMC and d) 1.7% CMC We notce that the swrls are becomng smaller and weaker wth the vscosty ncreasng. So they cannot reach the top and the bottom of the tank and secondary flow appears there and forms small swrls. The sze of those swrls becomes smaller wth the ncrease of the flud vscosty and dsappears fnally, whch confrm the fact that the decrease of vscosty led to a Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

5 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ better mxng. In fact, the flud s mxed above and below the turbne blades for the case of water contanng 0% of CMC, whch s explaned by the smaller frctonal forces and resstance forces, and when the vscosty ncreases we see that the upper swrl sze decreases and the lower swrl sze ncreases. On the other hand, the et delvered by the blade of the turbne s partcularly drected to the top of the tank as the vscosty s hgher. In the plane z = 0.20m we note that the velocty vectors, as a result of the ncrease n vscosty, s less drected to the vessel wall and defne parallel and concentrc streamlnes. Ths s due to the fact that for larger values of vscosty, the flow generated by the turbne s transent and not turbulent as t s the case for the water contanng 0% of CMC. As a confrmaton to our deductons, we see n Fg. 5 the global velocty of the flow, whch s less ntense n the entre tank for hgher values of vscosty. The maxmum velocty also decreased around the blades as a result of the ncrease n the shear stress due to the ncrease of vscosty. The dscharge of the turbne s moved up the tank for the hghest values of vscosty. The shear rate s defned by the followng equaton: τ = µγ [Pa]. In our case γ = 4.16 s -1, we wll then have the values of shear rate of the other studed vscous fluds gven n Table IV. TABLE IV SHEAR RATE FOR DIFFERENT VISCOSITIES CMC (%) τ [mpa] Fg. 5 Contours of the velocty magntude of the flow (m / s) of water contanng a) 0% CMC, b) 0.9% CMC, c) 1.1% CMC and d) 1.7% CMC Now we wll dscuss the flow feld behavor, wth the radal, axal and tangental velocty profles and contours, for the four studed case. The Rushton turbne s a radal flow mpeller, so t s mportant to focus on radal profles of the global velocty. Fg. 6 shows the radal profles of the global velocty n the horzontal plane located at the level of the blade (z = 0.20m) and the horzontal planes z =0.185m and z=0.215m located ust below and ust above the blade. Fg. 6 Radal profles of the velocty magntude (m / s) These planes were chosen because they better descrbe the flow feld near the blades, whch s the better mxng zone. At the blade level, the flud leaves the latter wth a velocty equal to U tp and decreases rapdly. For water, the decrease gradent n speed s smaller compared to the other three cases. The profles of the global velocty of CMC are all confounded above the blade and on the level of the blade. For the radal profle of the global velocty at the plane z = 0.215m, the speed s maxmum for the radal poston r = 0.08m n the case of water, whle for the varous solutons of CMC, t reaches ts Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

6 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ maxmum for the radal poston r =0.062m whch corresponds to the tp of the blade wth a value greater than that acheved by water alone. Ths s due to the nclnaton of the et delvered by the turbne blades up. Note that the velocty profles for dfferent CMC solutons are superposed and we do not really see the dfference between a vscosty of 16Cps and a vscosty of 32Cps above the turbne dsk. Just below the turbne dsk, we can see a dfference n the speed profle for the dfferent vscostes. The speed s much lower when the vscosty ncreases. Ths dfference s due to the fact that ths zone s almost stagnant, so any varaton of the radal speed s detected, as t s the case for the vscosty varaton. To better understand the behavor of the radal Rushton turbne, t s now nterestng to focus on the dstrbuton of the radal velocty, shown n Fg. 7. Fg. 7 Contours of the radal velocty (m / s) for water contanng a) 0% CMC, b) 0.9% CMC, c) 1.1% CMC and d) 1.7% CMC The dscharge moved upwards loses ts radal ntensty as t s the case for the decrease n the radal velocty across the tank wth the ncreasng vscosty. There s less reverse crculaton n the recrculaton loops and the wake drven by the turbne blades s less mportant when the vscosty ncreases. In the md plane and ust below the blade we noted that negatve veloctes occur n the case of CMC solutons. Ths creates a reverse flow manly due to et upward; we can see the effect of recrculaton loops top and bottom. It s also nterestng to consder the axal velocty of the flow n the strred tank. The radal profles of axal velocty n Fg. 8 show that the axal velocty correspondng to dfferent values of the vscosty does not dffer from each other, and as the radal velocty we also see that the case usng only water have a greater axal velocty for the same radal poston. Ths s due to the shear stress forces appled on the flud, and whch became more mportant as the flud vscosty ncrease. There s also a dfference n axal velocty ust below the dsc of the turbne where ts value for 1.7% CMC s equal to twce that noted for water alone. Ths s explaned by the fact that the adheson of the flud wth the turbne dsk s more mportant wth a hgh vscosty flud. Fg. 8 Radal profles of axal velocty (m / s) We conclude that the vscosty change affects manly the radal component and axal component of velocty. The flud rheologcal behavor sgnfcantly changes the appearance of the velocty profles and of the flud flow. Indeed, water, a Newtonan flud, creates a radal flow when agtated by a Rushton turbne, whle the flow generated by the same type of turbne turns to an axal flow for a non-newtonan flud and keeps smlar values when varyng vscosty. So dependng on our needs, we can create an axal flow behavor or a radal one, wth varyng the vscosty of our flud. But the mxng process s better wth a smaller vscosty, and we can mprove ths mxng wth changng the turbne poston by changng the turbne clearance. We now focus on the vscosty effect on the turbulence Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

7 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ feld, n the same medan planes. In Fg. 9, we see the dstrbuton of turbulent knetc energy k for dfferent vscostes. We notce that the turbulent knetc energy "k" s more mportant n zones of strong turbulence, whch s n the dscharge zone of the turbne. Away from the mxer, t gradually decreases to fnally vansh n the vcnty of the sde wall and the bottom of the tank, where no strong shear stress are noted. For the case of water contanng 0% of CMC, we have a strong turbulent knetc energy between two consecutve blades of the turbne, whch s due to the low adheson of the flud wth the turbne dsk whch consequently create an mportant turbulence n the vcnty of turbne blades. For the case of CMC solutons, ths rate change, and there are energy values greater all around the blade and part of that energy follows the drecton of the et delvered by the turbne. Fg. 9 Contours of turbulent knetc energy k (m²/s²) for water contanng a) 0% CMC, b) 0.9% CMC, c) 1.1% CMC and d) 1.7% CMC The maxmum values of k are even lower than the vscosty s hgh. It s also accurate to note that for the cases wth a percentage of CMC, the flow regme s transent, so the turbulence decreases wth the ncrease of vscosty, whch explan the contours of the turbulent knetc energy k obtaned. Ths s consoldated by the profles of the turbulent knetc energy, as we can see n Fg. 10. We see here, that above and below the turbne, the turbulent knetc energy of water wth 0% CMC s more mportant than the other three vscous fluds whch are confounded for the three postons of study. Fg. 10 Radal profles of the turbulent knetc energy k (m² / s ²) Agan here, we notce that ths turbulent parameter have the same behavor qualtatvely for the four fluds, ust below the blades, whch s explaned by the stagnant zone present under the turbne. At the level of the blade, the turbulence s more mportant for the water wth 0% CMC, and ths s due to the vscosty of the flud allowng a better mxng, so a more turbulent flud, wth an mportant gap on the tp of the blade. Note that the dfference between the curves n the case of dfferent concentratons of CMC s low, and at the plane z =0.215m we see that the turbulent knetc energy of vscous fluds s lower than the water turbulent knetc energy, and we note agan that t s much hgher when the flud vscosty ncrease whch can be explaned by the complex rheologcal Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

8 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ behavor of vscoelastc flud. To better understand the turbulent behavor of our flow feld, wth the vscosty varaton, we gve n Fg. 11 the contours of turbulence ntensty for the four studed cases. Fg. 11 Contours of turbulent ntensty (%) for water contanng a) 0% CMC, b) 0.9% CMC, c) 1.1% CMC and d) 1.7% CMC It shows that the turbulence s less ntense by ncreasng the vscosty. The appearance of the radal contours of the turbulence ntensty s smlar to that of the turbulent knetc energy, due to correlatons of proportonalty between I and 'k'. Below the blade, we see that the turbulence ntensty for dfferent vscostes remans unchanged whle at the level of the blade and above the blade, the turbulence s more ntense for the hgher values of vscosty then t decreases suddenly to become less than the water turbulence n the rest of the tank. These contours confrm our prevous nterpretatons: the more the flud s vscous, less s the turbulence. Ths s due to the fact that for vscous fluds contanng CMC, the flow regme s transent and the operaton of mxng s more dffcult and less perfect. IV. CONCLUSION The purpose of ths work was to brng out the effect of flud vscosty on the hydrodynamc parameters of the flow. We saw n ths work the conduct of a vscous flud, ts velocty, ts radal behavor and ts turbulent character. As results, we concluded that for a better mxng of our fluds, usng only water s advsed and we have then a turbulent radal flow. But f t s preferred to have an axal transent flow, we can ncrease the vscosty of the flud usng a gven percentage of CMC, the process of mxng s then athrst but the axal flow s favored. Changng the clearance of our turbne can amelorate the mxng and the hydrodynamc behavor of our flow feld. NOMENCLATURE C: Clearance, m C ε Emprcal constants of the k-ε model D: Impeller s dameter, m d: Dameter of the turbne s dsk, m E: Thckness of the turbne s dsk, m e p: Thckness of the blade, m G k : The generaton of turbulence knetc energy due to the mean velocty gradents G b : The generaton of turbulence knetc energy due to buoyancy H: Tank heght, m h: Lqud heght, m k: Turbulent knetc energy, m 2 s -2 l p : Blade wdth, m L p : Blade length, m N: Impeller rotaton speed, rpm N P : Power number N Q : Pumpng Number r : Poston vector n the rotatng sub doman s: Impeller submerson, m t: Tme, s T: Tank dameter, m U : component of the nstantaneous velocty vector, m/s u r : Relatve velocty vector u : Absolute velocty vector x : Absolute poston n Cartesan coordnates x Orgn of the axs of rotaton of the rotatng feld 0 z: Axal poston, m Greek Symbols ρ : Flud densty, kg/m 3 µ : Flud dynamc vscosty, Pa.s µ t : Turbulent vscosty, Pa.s ε : Turbulent energy dsspated per unt mass, m 2 s -3 σ k,σ ε : Emprcal constants of the k-ε model Y M : The contrbuton of the fluctuatng dlataton n compressble turbulence β : Coeffcent of thermal expanson Ω : Angular velocty vector REFERENCES [1] C. Gómez, C. P. J. Bennngton, and F. Taghpour. Investgaton of the Flow Feld n a Rectangular Vessel Equpped Wth a Sde-Enterng Agtator. J. Fluds Eng., , [2] S Y. Lee and Rchard A. Dmenna. Applcatons of CFD Method to Gas Mxng Analyss n a Large-Scaled Tank. ASME Conf. Proc., FEDSM2007. [3] Robert A. Leshear, S Y. Lee, Mark D. Fowley, Mchael R. Porer, and Tmothy J. Steeper. Comparson of Experments to Computatonal Flud Dynamcs Models for Mxng Usng Dual Opposng Jets n Tanks Wth and Wthout Internal Obstructons. J. Fluds Eng., , [4] Paul A. Glls, Gerrt Hommersom, and Matthas Schäfer. A Comparson of Several CFD Approaches for Predctng Gas-Lqud Contactng n a Cylndrcal Tank Agtated Wth a Sngle Rushton Turbne. ASME Conf. Proc., PVP2002. [5] Ranade, V.V.. An effcent computatonal model for smulatng flow n strred vessels: case of Rushton turbne. Chem Eng Sc,, Vol. 52, 24, [6] NG, K. et al. Assessment of sldng mesh CFD predctons and LDA measurements of the flow n a tank strred by a Rushton mpeller. TransI Chem E., Vol. 76, parta, [7] Kumaresan, T et al. Effect of mpeller desgn on the flow pattern and mxng n strred tanks. Chem Eng Sc,, [8] Mavors, P.. Flow vsualzaton n strred vessels-a revew of expermental technques. TransI ChemE., Vol. 79, part A, Internatonal Scholarly and Scentfc Research & Innovaton 7(3)

9 World Academy of Scence, Engneerng and Technology Internatonal Journal of Mechancal and Mechatroncs Engneerng Internatonal Scence Index, Mechancal and Mechatroncs Engneerng waset.org/publcaton/ [9] Zadghaffar, R. et al. Large Eddy Smulaton of turbulent flow n a strred tank drven by a Rushton turbne. Computer & Fluds, Volume 39, Issue 7, [10] Lu, W. et Yang, B.. Effect of blade on the structure of the tralng vortex around Rushton turbne mpellers. Can. J. Chem. Eng., Vol. 76, [11] Ocheng,A. et al. Mxng n a tank strred by a rushton turbne at a low clearance. Chem. Eng. Process, Vol. 47, [12] Brucato, A et al. Numercal predcton of flow felds n baffled strred vessels: A comparson of alternatve modelng approches. Chem Eng Sc,, Vol. 53, 21. [13] NG, K. et Yannesks, M.. Obsevatons on the dstrbuton of energy dsspaton n strred vessels. TransI ChemE,, Vol. 78, part A, [14] Mavros, P et al. Determnaton of flow felds n agtated vessels by Laser-Doppler Velocmetry: Use and nterpretaton of RMS veloctes. Trans IChemE,, Vol. 76, part A, [15] Yundong, W. et al. PIV measurements and CFD smulaton of vscous flud flow n a strred tank agtated by a Rushton turbne. Melbourne, Australa: CSIRO, Ffth Internatonal Conference on CFD n the Process Industres, [16] Trven, B. et al. Mxng studes of non newtonan fluds n an anchor agtated vessel. Chem. Eng. Res. Des.,, Vol. 88, Internatonal Scholarly and Scentfc Research & Innovaton 7(3)