Computational simulation of fluid dynamics in a tubular stirred reactor

Transcription

1 Computatonal smulaton of flud dynamcs n a tubular strred reactor CAO Xao-chang( 曹晓畅 ), ZHANG Tng-an( 张廷安 ), ZHAO Qu-yue( 赵秋月 ) School of Materals and Metallurgy, Northeastern Unversty, Shenyang , Chna Receved 21 May 2008; accepted 10 October 2008 Abstract: The flow and concentraton felds n a new style tubular strred reactor were smulated by smulatng the fluds dynamcs(cfd), n whch FLUENT software was used and the standard k ε model and multple reference frame(mrf) were adopted. The varous values of ntal rotatng speed and nlet flow rate were adopted. Smulatons were valdated wth expermental resdence tme dstrbuton(rtd) determnaton. It s shown that the flud flow s very turbulent and the flow pattern approaches to the plug flow. The velocty ncreases from shaft to the end of mpeller, and the gradent s enlarged by ncreasng the rotatng speed. Comparson between RTD curves shows that agtaton can mprove the performance of reactor. As the flow rate ncreases, the mean resdence tme decreases proportonally, and the varance of RTD lessens as well. When rotatng speed ncreases to a certan value, the varance of RTD s enlarged by ncreasng rotatng speed, but the mean resdence tme has no obvous change. Key words: computatonal flud dynamcs(cfd); resdence tme dstrbuton(rtd); tubular strred reactor 1 Introducton Reactor s the key pece of equpment n all hydrometallurgcal dgeston process. In the current study, an nnovatve tubular strred reactor was examned, and t s possble that such a reactor would have many applcatons. The reacton knetcs and the yeld are, to a great extent, decded by the type and the sze of the reactor, and thus the selecton, desgn, calculaton and the optmzaton condtons are of mportance n the chemcal and metallurgcal producton. Based on the prncple of rasng effcency, reducng nvestment and producton costs, a new style mult tubular reactor was developed n Northeastern Unversty(NEU), Chna, usng the theory of agtaton mxng. The concept desgn ams to overcome some of the dsadvantages of the tradtonal tubular reactors that are ndustrally avalable. An agtaton devce s smply added to the tradtonal tubular reactor and sxteen groups of T-type blades are dstrbuted unformly n the agtatng shaft. These blades have the functon of strengthenng the mxng effects, and the transverse blades can help contnually to scrape the wall and thus decrease or even elmnate scabs. Computatonal flud dynamcs(cfd) s an effectve approach for the desgn and optmzaton of the strred reactor[1 5], and has been frequently used n the analyss of the reactor characterzaton n varous applcatons n recent years[6 8]. In ths study, a commercal code FLUENT 6.3 (FLUENT Inc.) was used to smulate the new style strred reactor wth nlet mass flow at varous rotatng speeds, and the resdence tme dstrbuton(rtd) and flow feld were nvestgated. The objectve of the present study s to characterze the flow behavor of tubular strred reactor. CFD predctons are valdated wth expermental RTD curves. The CFD analyss can mprove the performance of the reactor and reduce testng n experments. 2 Expermental The strred vessel nvestgated s a tubular reactor wth a mult-bladed mpeller, as schematcally shown Fg.1. The cylndrcal vessel s 2 m n length and m n dameter; and the nlet and outlet dameters are 0.04 m. The mpeller s composed of sxteen groups of T-type blades wth 0.09 m n heght and 0.12 m n wdth, each of whch s 0.09 m n heght and 0.1 m n wdth. Water at 25 was used as the test flud. The reactor was flled by water when mass flow rates at nlet and outlet were montored and controlled by the mass flow meter. Foundaton tem: Project( ) supported by the PhD Program Foundaton of Mnstry of Educaton of Chna; Project supported by the Foundaton of Excellent Talents of Scence and Technology of Laonng Provnce, Chna Correspondng author: ZHANG Tng-an; Tel: ; E-mal: zta2000@163.net DOI: /S (08)

2 490 CAO Xao-chang, et al/trans. Nonferrous Met. Soc. Chna 19(2009) Fg.1 Schematc maps of expermental setup (a) and mpeller (b) The RTDs were determned expermentally by adoptng the classcal tracer response technque[9]. Dfferent mpeller speeds and nlet mass flow rates were nvestgated n the mxng experments. An nert chemcal tracer was njected nto the reactor promptly when the flow tended to steady; meanwhle, measurements of soluton conductance were carred out usng conductvty meter. The effluent conductance tme curve s referred as concentraton(c) curve n RTD analyss, and C(t) s dvded by the ntegral to obtan the E(t) curve from C(t) curve. The dmensonless RTD functon E(θ) was also used by defnng the dmensonless tme n the followng form: E(θ)= t E(t) (1) t where θ(= t ) s the dmensonless tme; and t ( t = te ( t)dt ) s the mean resdence tme. 0 3 Numercal smulaton The numercal smulaton was carred out usng a commercal CFD package ANSYS FLUENT, whch s based on fnte-volume methods. 3D geometry s created and meshed usng the commercal grd-generaton tool GAMBIT software (FLUENT Inc.) wth tetrahedral elements, contanng cells totally. Part of grd of tubular strred reactor s shown n Fg.2. Compared wth the numercal predcton, the amount of mesh s adequate for ths smulaton. Fg.2 Part of grd of tubular strred reactor The predcton of turbulent flow s based on the numercal soluton of the tme-dependent, threedmensonal, Reynolds-averaged contnuty and Naver-Stokes equatons. The standard k-ε model has been wdely used for modelng turbulent flow n the strred reactor and t s the most common turbulence model for analyzng engneerng flows. The varatons of the k-ε model such as Renormalzed Group(RNG) k-ε model, whch can gve superor results for sotropc turbulence, s also appled n flow predctons n strred reactors, but there are only slght changes n turbulence predctons. RNG k-ε model can gve superor results for sotropc turbulence. Large Eddy Smulaton(LES) for modelng flow n the strred reactor shows good agreement wth expermental data for both veloctes and turbulence quanttes. However, due to the assocated computatonal expense and lmtatons of grd requrements, LES model s mpractcal for many

3 CAO Xao-chang, et al/trans. Nonferrous Met. Soc. Chna 19(2009) research requrements[10]. Hence, the standard k-ε model was used n ths work. The governng equaton for turbulent knetc energy, k, and turbulent energy dsspaton rate, ε, are wrtten as: k ( ρk) + ( ρuk) = ( μ + μ t / σ k ) + G ρε (2) t t ε ρε ) + ( ρuε ) = ( μ + μ / σ ε ) + ( t ( 2 c1g c ρε ) (3) where μ t s turbulent vscosty and G s turbulence generaton rate. 2 k μe = ρcμ (4) ε G=μ t [(u y +v x ) 2 +(v z +w y ) 2 +(w z +u z ) 2 +2(u x +v y +w z ) 2 ] (5) The standard k-ε model constants are: c 1 =1.44, c 2 = 1.92, c μ =0.09, σ k =1.0, σ ε =1.3. For smulatng the flows generated by the mpeller, there are two common approaches: one s Multple Reference Frame(MRF), and the other s Sldng Mesh (SM) approach. Usually, the MRF method s for steady-state flow whle SM s for unsteady flow[11]. In ths work, the MRF model has been shown to perform well for ths confguraton, and thus was selected. The whole vessel s dvded nto two regons: the mpeller zone and the statonary zone. The soluton s matched at the nterface between the rotatng and the statonary regon va velocty transformaton from one frame to the other. In ths way, the equatons for the fxed and the rotatng part of the mesh were solved separately and the effects of the blade rotaton were accounted by vrtue of the reference frame. The convecton term n the governng equatons was modeled wth the bounded second-order scheme and SIMPLE algorthm was used to resolve the couplng between velocty and pressure[12]. The crtera of 10 4 were set for the resduals of contnuty, veloctes, k, and ε equatons to determne the convergence of soluton, wth ths value beng consdered suffcent to have a converged smulaton. All smulatons were carred out by a workstaton equpped wth two Intel Xeon 3.0 Hz processors, 16GB RAM, usng parallel technque n FLUENT. In the experments, water was used as the test flud. The smulaton of RTD has been carred out by njectng a pulse of a tracer at the nlet. The two-speces transport model was appled n RTD predcton. A sngle-speces flow feld was frst obtaned under steady-state model. The tracer wth the same propertes as the water was ntroduced at the entrance wth a momentary pulse usng transent model. In ths way, the C/C 0 can be obtaned drectly from the results of the outlet. 4 Results and dscusson 4.1 Analyss of flud feld In Fg.3, the results of the smulaton are presented graphcally (Q=1.8 m 3 /h, N=150 r/mn). Under the effect of agtaton, the dstrbuton of velocty shows that the flow feld s very turbulent. In the llustraton of segmental system, the flud flows along the shaft n helcal, and axal mxng s generated by the rotatng mpeller. It can be seen from part of vector plot of velocty that agtaton can accelerate the flow near wall surface of reactor, whch can prevent the appearance of scalng. Fg.4 shows the comparson of Z-axal velocty n dfferent radal dstances at dfferent rotatng speeds (Q=1.8 m 3 /h), and Fg.5 shows the radal velocty at dfferent rotatng speeds n the center of the vessel. It s demonstrated that the velocty magntude ncreases from shaft to the ends of the mpeller. As the mpeller speed ncreases, flud-resstance appears near wall surface by means of centrfugal force. The velocty magntude s well dstrbuted at N=50 r/mn for low centrfugal force. Fg.3 Contour plot of velocty (a) and part of vector plot of velocty (b) (Q=1.8 m 3 /h, N=150 r/mn)

4 492 CAO Xao-chang, et al/trans. Nonferrous Met. Soc. Chna 19(2009) Fg.5 Radal velocty n dfferent mpeller speeds at flow rate of 1.8 m 3 /h Fg.4 Comparson of Z-axal velocty n dfferent radal dstances at flow rate of 1.8 m 3 /h: (a) 50 r/mn; (b) 150 r/mn; (c) 250 r/mn Dfferent optmum mpeller speeds are obtaned at dfferent nlet flow rates. The optmum mpeller speed s 50 r/mn whle nlet flow rate s 1.8 m 3 /h. 4.2 Characterstcs and profles of RTD functons The expermental C(t) curves were used to obtan nformaton about the mean flud resdence tme, the varance of dstrbutons, σ 2, and the RTD dstrbuton functons at the reactor ext, nclusvely n normalzed form E(θ). The E(θ) curves show the presence of stagnant zones. When the maxmum of E(θ) appears at θ<1, t ndcates the presence of short-crcuts; whle the maxmum of E(θ) appears at θ>1, t ndcates the presence of the back mxng. The wdth of RTD curve s an approprate measurement to determne the approach to plug flow[13 15]. Fg.6 shows the comparson of the RTD curves by smulatons wth expermental data, n whch the two are accordant, especally at low rotatng speed, ndcatng that CFD approach used n ths work s relable for smulatng the RTD curves of the tubular strred reactor. Fg.7 shows the expermental RTD curves n the tradtonal tubular reactor at nlet flow rate of 1.8 m 3 /h, and Fg.8 shows the numercal RTD curves at dfferent mpeller speeds. Several maxmums of the curve appear wth no strrng by experment, whle only one maxmum by CFD predcton. The result s optmzed by model smplfcaton for nterface between tubes on smulaton. By comparng wth no strrng, the RTD curve s narrow wth strrng, where the flow s shown to approach to plug flow condtons. Although slow strrng can narrow the RTD curve and mprove the performance of the reactor, ncreasng mpeller speed wdens the RTD curve. Maxmum of E(θ) offsets to θ<1 at mpeller speed of 400 r/mn, ndcatng the presence of the short- crcuts. Hgh mpeller speed can worsen reactor performance. The maxmum of the curve E(θ) appears near θ=1 at mpeller speed of 50 r/mn, and flow pattern tends to deal plug flow. Table 1 shows the comparson between smulated and expermental data of mean resdence tme and varance. For exstng error and model smplfcaton, numercal predcton s a lttle lower n mean resdence

5 CAO Xao-chang, et al/trans. Nonferrous Met. Soc. Chna 19(2009) Fg.6 Comparson of RTD curves between smulatons and expermental data

6 494 CAO Xao-chang, et al/trans. Nonferrous Met. Soc. Chna 19(2009) Table 1 Comparson between numercal and expermental data of mean resdence tme and varance Flow rate, Impeller speed, Mean resdence tme, t/ s Varance, σ 2 Q/(m 3 h 1 ) N/(r mn 1 ) Smulated Expermental Smulated Expermental the varance ncreases sharply, ndcatng that the flud flow devates from the deal plug flow. There are several nfluencng factors of mean resdence tme. In CFD predcton, as the rotaton speed ncreases, there s no evdent effect on the mean resdence tme. But n experments, the result shows that the mean resdence tme decreases wth ncreasng rotatng speed. For the centrfugal force generated by hgh rotatng speed, crculaton dead zone appears near wall surface of vessel and most flud flows forward along strrng shaft to outlet drectly. Moreover, as nlet flow rate ncreases, changng rotatng speed brngs no clear effect on the mean resdence tme. Fg.7 Expermental RTD curves n tradtonal tubular reactor at nlet flow rate of 1.8 m 3 /h Fg.8 Typcal RTD curves at dfferent mpeller speeds at nlet flow rate of 1.8 m 3 /h tme. But the result shows a good agreement n the whole trend, whch provdes postve reference sgnfcantly. It can be seen form Table 1, as the nlet flow rate ncreases, the mean resdence tme and the varance of RTD decrease proportonally. As the rotaton speed ncreases, 5 Conclusons 1) The CFD smulaton of flow feld and RTD n a tubular strred reactor usng the standard k-ε turbulence model and MRF rotatng model was nvestgated. The RTD curves predcted wth CFD model show good agreement wth expermental data. 2) The dstrbuton of velocty shows that the flow feld s very turbulent and the flud flows along the shaft n helcal shape. The velocty magntude ncreases from shaft to the ends of mpeller, and the hgher the mpeller speed s, the larger the gradent of veloctes magntudes. 3) The tubular reactor wth a strrer can mprove the flow profle by narrowng the RTD curve, decreasng mean resdence tme and avodng back mxng, but a hgh strrng speed broadens the RTD curve drastcally. The optmum rotatng speed s 50 r/mn whle nlet flow rate s 1.8 m 3 /h. 4) The RTD functons demonstrate that the profles of flow approach to plug flow. As the flow rate ncreases, the mean resdence tme as well as the varance of RTD decreases proportonally. As the rotaton speed ncreases, there s no evdent effect on the mean resdence tme, whereas the varance s enlarged greatly.

7 CAO Xao-chang, et al/trans. Nonferrous Met. Soc. Chna 19(2009) References [1] ZHANG Q, JIN Jun-ze, WANG Tong-mn, LI Tng-ju, GUO Qng-tao. Analyss of molten metal flow n rotatng magnetc feld [J]. The Chnese Journal of Nonferrous Metals, 2007, 17(1): (n Chnese) [2] SWAINE D E, DAUGULIS A J. Revew of lqud mxng n packed bed bologcal reactors [J]. Botechnol Prog, 1998, 4: [3] RANADE V V, DOMMETI S M S. Computatonal snapshot of flow generated by axal mpellers n baffled strred vessels [J]. Trans IChemE, 1996, 74(4): [4] STAMOU A I. Improvng the hydraulc effcency of water process tanks usng CFD models [EB/OL]. Chemcal Engneerng and Processng, 2007, do: [5] TORRE J P, FLETCHER D F, LASUYE T, XUEREB C. Sngle and multphase CFD approaches for modellng partally baffled strred vessels: Comparson of expermental data wth numercal predctons [J]. Chemcal Engneerng and Scence, 2007, 62: [6] DARELIUS A, RASMUSON A, van WACHEM B, NIKLASSON I, FOLESTAD S. CFD smulaton of the hgh shear mxng process usng knetc theory of granular flow and frctonal stress models [J]. Chemcal Engneerng Scence, 2008, 63: [7] PAKZAD L, EIN-MOZAFFARI F, CHAN P. Usng electrcal resstance tomography and computatonal flud dynamcs modelng to study the formaton of cavern n the mxng of pseudo plastc fluds possessng yeld stress [J]. Chemcal Engneerng Scence, 2008, 63: [8] OCHIENG A, ONYANGO M S, KUMAR A, KIRIAMITI K, MUSONGE P. Mxng n a tank strred by a Rushton turbne at a low clearance [J]. Chemcal Engneerng and Processng, 2008, 47: [9] ZHAO Qu-yue, ZHANG Tng-an, CAO Xao-chang, JIANG Xao-l. RTD curves of tubular reactor wth strrer [J]. Journal of Northeastern Unversty: Natural Scence, 2006, 27(2): [10] DEGLON D A, MEYER C J. CFD modelng of strred tanks: Numercal consderatons [J]. Mnerals Engneerng, 2006, 19: [11] XIA J Y, WANG S J, ZHANG S L, ZHONG J J. Computatonal nvestgaton of flud dynamcs n a recently developed centrfugal mpeller boreactor [EB/OL]. Bochem Eng J 2007, do: / j.bej [12] JAVED K H, MAHMUD T, ZHU J M. Numercal smulaton of turbulent batch mxng n a vessel agtated by a Ruston turbne [J]. Chemcal Engneerng and Processng, 2006, 45: [13] GAVRILESCU M, TUDOSE R Z. Resdence tme dstrbuton of the lqud phase n a concentrc-tube arlft reactor [J]. Chemcal Engneerng and Processng, 1999, 38: [14] SAHLE-DEMESSIE E, BEKELE S, PILLAI U R. Resdence tme dstrbuton of fluds n strred annular photo reactor [J]. Catalyss Today, 2003, 88: [15] KUMAR V, NIGAM K D P. Numercal smulaton of steady flow felds n coled flow nverter [J]. Internatonal Journal of Heat and Mass Transfer, 2005, 48: (Edted by YANG Bng)