Agitation and mixing are important in a wide variety

Transcription

1 ChE labratry An Agitatin Experiment With Multiple Aspects Jrdan L. Spencer Department f Chemical Engineering Clumbia University, New Yrk Agitatin and mixing are imprtant in a wide variety f areas in bth the traditinal and mdern prcess industries, [1] and it is apprpriate that chemical engineering students see related experiments in the unit peratins labratry. This paper describes a teaching experiment invlving bth agitatin and mixing that illustrates using a quite simple and relatively inexpensive apparatus a number f aspects f this field. In particular the experiment invlves nt nly simple and direct measurements, fr example f trque and pwer as functins f stirring speed, but als mre sphisticated data-acquisitin and prcessing methds, fr example indirect measurement invlving the use f a mdel and a parameter estimatin methd. APPARATUS The apparatus is shwn schematically in Figure 1 (next page). The majr cmpnents f the apparatus are: A trque table, cnsisting f a 12-inch-diameter aluminum circle munted n a tapered rller bearing set in a 12-inch-square aluminum base plate. Even with a lad f abut 20 kg, the trque needed t set the upper plate in mtin is less than N m (1 z inch). An arm attached t the upper plate bears a lad cell (Omega Engineering, Mdel LCGC) cnnected t a panel meter (Omega Engineering). The data are acquired by a LabView prgram at 0.2-secnd intervals. A variable speed DC mtr (Cle-Parmer) with speed cntrller and trque indicatin. The speed can be varied frm 60 t 2400 RPM, and the maximum trque is 45 z-in (0.318 N m). Tw six-bladed turbines (f diameter 14.4 and 7.5 cm and blade width 3.32 and 1.83 cm), and tw threebladed prpellers f diameter 14.4 and 7.5 cm. All are munted n 3/8-inch glass-epxy shafts inserted in a chuck n the mtr shaft. A plycarbnate tank f ID 29.2 cm and vlume abut 18 L. This tank is equipped with fur remvable stainless baffles f width 2.43 cm, munted n an acrylic tp plate. A stainless funnel is munted near the tp f the tank, t be used fr adding a cnductive tracer, fr example NaCl r KCl at 30 g/l. A platinum electrde cnductivity cell is munted near the bttm f the tank 180 degrees frm the funnel. The cell is cnnected t a cnductivity meter (Amber Sciences) that sends a 0- t Jrdan L. Spencer is emeritus prfessr f chemical engineering at Clumbia University. He received his B.S. in 1953 and his Ph.D. in 1961, bth frm the University f Pennsylvania and bth in chemical engineering. His research and teaching interests invlve cntrl and ptimal cntrl, and the develpment f chemical engineering teaching experiments, including Web-perable experiments. Cpyright ChE Divisin f ASEE 2006 Summer

2 FUNNEL OPTICAL SENSOR LAMP CEE01 DC MOTOR BEAD IMPELLER TORQUE TABLE MOTOR CONTROLLER TANK WITH BAFFLES CONDUCTIVITY CELL LOAD CELL Figure 1. Schematic diagram f the apparatus, shwing baffled tank n trque table with lad cell, mtr and impeller, cnductivity prbe, funnel fr tracer additin, and ptical sensr and lamp fr bead detectin. Trque (N m) RESULTS RPM Figure 2. Trque as a functin f turbine speed fr water in baffled 18-liter tank. Als shwn is a curve f the frm Trque: k RPM 2. 1-vlt signal t the cmputer. A phttransistr (OPF-703) munted n the side f the tank 3 cm frm the bttm is used t detect the apprach f almst neutrally buyant 0.9 cm tridal plastic beads. The fluid near the sensr is illuminated by a 20 Watt desk lamp. A secnd plycarbnate tank f inner diameter 17.5 cm, als equipped with fur stainless baffles, and with vlume abut 4 L. All dimensins f the smaller tank/impeller cmbinatin are prprtinal t the dimensins f the larger tank/impeller cmbinatin, with a factr f A heat transfer prbe cnstructed by inserting a 90 W resistance heater in the center f a 5-cm-diameter by 7.5-cm-lng aluminum cylinder. A transistr-based temperature sensr (LM35-CAZ) is als munted, ff-center, in the cylinder. The prbe culd be suspended near the middle f the 20 L tank, abut 5 cm frm the wall. Presented belw are sme typical results, with cmments related t what the results illustrate fr the student. Trque and Pwer The 18-liter tank was filled with water t a depth f 25 cm. With the baffles in place and the 7.5-cm-diameter turbine munted in the mtr, the stirring speed was varied ver a range f RPMs. The trque was measured by the lad cell and averaged by a LabView prgram. Typical results are shwn in Figure 2, where the trque (N m) is pltted as a functin f RPM. Als shwn is a curve f the frm Trque = k RPM 2, which fits the data almst perfectly, as expected. [1] Since the trque signal was fund t vary with time (with an amplitude abut 10% f the average trque), especially at high RPM where the flw in the tank is quite turbulent, it was f interest t lk at the pwer spectra f the data. A typical spectrum (Figure 3) shws that mst f the pwer is at lw frequencies, less than 0.15 cycles/sec. It is prbable that the fluctuatins reflect the presence f eddies r vrtices generated by the impeller. Pwer Frequency (dimensinless) Figure 3. Pwer spectrum f trque signal fr 7.5-cm turbine in 18-liter baffled tank at 800 RPM. Nn-Newtnian and High Viscsity Fluids In rder t examine the behavir f a nn-newtnian liquid, the 4-liter tank (with baffles) was filled t a depth f 15 cm with cmmercial ketchup. The 7.5-cm-diameter flat-bladed turbine was used t stir the ketchup. At 200 RPM the surface f the ketchup was statinary, clearly a nn-newtnian behavir. At 400 and 800 RPM the ketchup flwed smthly at the surface. The data were well, but nt perfectly, fitted by a curve f the frm Trque = k RPM 2. Data were als cllected under the same cnditins using crn syrup (Kar), a Newtnian fluid with a viscsity abut 2,500 times that f water. Fr these runs the trque was a linear functin f the RPM, as expected. Chemical Engineering Educatin

3 Tracer Studies f Mixing Times Mdeling and Parameter Estimatin Mixing times have been estimated [1, 2] by visual bservatin fllwing the additin f a dye r cnductive tracer t the agitated liquid. This methd, while satisfactry in sme cases, has the disadvantage that it is inherently subjective, and cannt be used with cludy r paque fluids. A mre bjective methd is based n acquiring and prcessing cnductivity data fllwing the additin f a cnductive tracer (e.g., NaCl slutin) t the agitated fluid in the baffled r unbaffled 18-liter tank. The data are acquired by a LabView prgram, typically 100 baseline pints in 20 secnds, fllwed by 400 cnductivity pints in 40 secnds. The tracer data are saved frm Excel as a space-delimited (.prn) file readable by a QuickBASIC parameter estimatin prgram. The mdel used t fit the data, shwn in Figure 4, cnsists f six well-mixed tanks. Three, f equal vlume, crrespnd t dwnward-mving fluid in the cre f the tank. The ther three tanks (all f the same vlume) crrespnd t the fluid mving upward alng the walls f the tank. Symmetry arund the prpeller shaft is assumed, s that nly three shell tanks are shwn. Salt slutin injectin is assumed t take place at the upper right, and a cnductivity prbe is lcated at the lwer left. The mdel cntains tw undetermined parameters, dented b 1 and b 2, with b 1 the fractin f the knwn tank vlume in the three cre tanks, and b 2 the vlumetric flw rate (L/s) dwnward thrugh the cre tanks and upward thrugh the shell tanks. The vlume f a cre tank is b 1 V/3, and the vlume f a shell tank is (1 b 1 )V/3. An bjective mixing time is three times the tank vlume, dented V, divided by b 2. CONDUCTIVITY PROBE CORE TANKS SHELL TANKS B2 B1 V/3 (1 - B1) V/3 (1 - B1) V/3 (1 - B1) V/3 Figure 5 shws the nrmalized cnductivity vs. time data fr salt slutin injectin int the 18 L DATA tank, with agitatin prvided by a 7.5-cm-diameter 1.5 dwnward-driving prpeller rtating at 60 RPM. Als shwn is the best-fit curve crrespnding t 1.0 the mdel discussed abve. The best-fit parameter BEST FIT values were b 1 = and b 2 = L/s. The 0.5 cnductivity des nt rise fr abut five secnds, crrespnding t the time needed fr the salt slutin t mve frm the wall f the tank t the 0.0 center, dwn t the bttm f the tank, and then ver t the cnductivity prbe lcated ppsite the Time (secnds) injectin pint. Then the cnductivity rises and drps rapidly as the blus f salt slutin passes the prbe. After sme further scillatins the Figure 5. Cnductivity data vs. time, and best-fit respnse frm cnductivity reaches a cnstant value. The curve mdel, fr tracer injectin int 18-liter baffled tank at 60 RPM using based n the six-pl mdel fits the data fairly 7.5 cm prpeller. Parameters: b 1 =0.484, b 2 =1.368 L/s. well, but certainly nt perfectly. This is because Summer Cnductivity B1 V/3 B1 V/3 B2 SIX-POOL MODEL OF FLOW PATTERN INJECTION POINT Figure 4. Six-pl mdel f the flw pattern in the tank, used fr analysis f cnductive tracer-injectin data. The cre pls (tanks) represent the dwnward-flwing liquid in the center f the tank, the shell pls represent the upwardflwing fluid near the tank wall. Parameter b 1 is the fractin f the tank vlume V in the cre, and b 2 is the vlumentric flw rate (L/s) thrugh the array f well-mixed tanks. The state variables are the tracer cncentratins in the six tanks. cee05

4 At high Reynlds numbers the flw in the tank is, at least in sme sense, strngly turbulent. This implies that particles suspended in the tank mve in a chatic and uncrrelated way, and thus mve independently. prached high values. This reflects the fact that the resistance t heat transfer is the sum f a cnstant resistance due t the aluminum wall f the prbe, and a film resistance at the prbe surface that varies with the 2/3 pwer f RPM. Frm the high RPM asymptte the first resistance can be calculated, and frm a secnd pint the heat transfer cefficient can be fund as a functin f RPM. In general the results were cnsistent with Eq. (1): k = a N 0.67 = a N 2/3 (1) where k is the heat transfer cefficient (Wm 2 / C), a is a cnstant, and N is the stirring speed (s -1 ). cee06 the mdel is much t simple t crrespnd exactly t the highly turbulent, three-dimensinal, and cmplex flw pattern actually existing in the baffled tank, even at lw RPM. The parameter b 1 (the fractin f tank vlume) was 0.484, and b 2 (the circulatin rate) was L/s. When the stirring speed was dubled t 120 RPM the cnductivity rse much earlier, versht less, and settled ut abut three times mre rapidly crrespnding t mre vigrus mixing. The value fr the circulatin rate parameter b 2 was 2.765, mre than duble that fr the 60 RPM run. Similitude In thery, fr tanks that are gemetrically similar, at the same Reynlds number the pwer numbers shuld als be equal. As a test f this thery, the trque is measured at 600 RPM using water and a flat-bladed turbine in the 4-liter baffled tank, and the Reynlds number is calculated. Then the trque is measured in the gemetrically similar 18-liter tank, at an RPM crrespnding t the same Reynlds number. When the experiments were perfrmed, the calculated and measured trques typically agreed within 20%. Heat Transfer Cefficient It is well dcumented [1, 2] that heat transfer cefficients in agitated tanks depend strngly n the intensity f agitatin. In rder t demnstrate this, the heat transfer prbe was immersed in water in the baffled 18 L tank. The pwer t the prbe was turned n, the stirring speed was set, and the prbe temperature was allwed t cme t steady state, which ccurred in a few minutes. The difference between the prbe and water temperature was pltted as a functin f RPM. As expected, the temperature difference was highest at 0 RPM, drpped mntnically as RPM increased, and apprached a nnzer cnstant as the RPM ap- 162 Optical Sensr Signal Figure 6. Optical sensr vltage fr beads in 18-liter tank at 400 RPM. Each drp in vltage crrespnds t the entry f a bead int the field f view f the phttransistr. Only drps belw a selected vltage are cunted as events. Ln(interval density) Time (secnds) cee Interval Length (secnds) Figure 7. Semilg plt f distributin f bead arrival intervals. The straight line crrespnds t a Pissn distributin. Chemical Engineering Educatin

5 Nte that all real-wrld measurements invlve bth signal and nise. In mst cases the infrmatin is cntained in the signal and we attempt t minimize the nise. But in sme cases the nise als cntains useful infrmatin. The results... illustrate this. Particle Dynamics At high Reynlds numbers the flw in the tank is, at least in sme sense, strngly turbulent. This implies that particles suspended in the tank mve in a chatic and uncrrelated way, and thus mve independently. In rder t test this predictin abut 200 plastic tridal beads f apprximate diameter 0.9 cm were added t the tank. The 7.5-cm turbine was run at 400 and 800 RPM. A typical sensr signal is shwn in Figure 6, crrespnding t a sample rate f 100 per secnd. Each drp in vltage represents the entries f ne r mre beads int the illuminated regin. The prgram that acquired the data als used simple lgic t identify clse-bead appraches, t calculate the time interval between entry, and t cnstruct an interval distributin functin. If the beads in fact mve independently, this is expected t be a Pissn distributin. Typical results, shwn in Figure 7 in a semilg plt, crrespnd reasnably well t a straight line and thus t a Pissn distributin. The slpe f the line is related t the average frequency f bead events, but als depends n the efficiency f detectin f bead appraches, which is nt easily knwn. The lwer values at lw time intervals prbably crrespnd t the fact that the data acquisitin prgram is nt able t differentiate between tw r mre bead entries that ccur at almst the same time. Nte that all real-wrld measurements invlve bth signal and nise. In mst cases the infrmatin is cntained in the signal and we attempt t minimize the nise. But in sme cases the nise als cntains useful infrmatin. The results abve illustrate this. Salt Crystal Disslutin When a crystal f a sluble salt, fr example NaCl, sits in water that is nt mving, it disslves relatively slwly. But the ppsite hlds fr a crystal suspended in strngly turbulent water. Apprximately ne gram f a carse (abut 150 crystals per gram, the crystals being f variable size) kitchen salt was added t water in the baffled 18 L tank. At 0 RPM full disslutin required mre than 60 minutes. The signal frm the cnductivity prbe recrded by a LabView prgram is shwn in Figure 8. Using the 7.5-cm-diameter turbine, disslutin was almst twice as fast at 800 RPM as at 400 RPM. These results demnstrate that the apparatus described abve can be used in a wide variety f studies f the effect f stirring speed, impeller design, and ther parameters n the rate f disslutin f (r extractin frm) slids, as lng as the slids release a cnductive tracer. CONCLUSIONS The agitatin and mixing experiment described abve is based n a relatively simple and inexpensive apparatus. But it illustrates a number f aspects f the subject, including the cee08 Cnductivity Figure 8. Cnductivity as a functin f time fllwing additin f 1 gram f NaCl crystals t the agitated 18-liter baffled tank at 400 RPM Time (secnds) Summer

6 dependence f trque n stirrer speed, impeller design, baffle design, and nature f the fluid invlved. The principle f similitude can be tested. The experiment als illustrates very general and mre sphisticated cncepts, including the use f mdern data acquisitin sftware and nnlinear regressin methds t estimate the parameters f a mdel f the flw pattern in an agitated vessel. The apparatus is well adapted t studying the rate f disslutin f salt crystals, and the effect f agitatin intensity n heat transfer frm a slid surface. Finally, students are able t acquire and prcess essentially stchastic data t btain sme infrmatin n the turbulent flw in the vessel. REFERENCES 1. McCabe, W.L., J.C. Smith, and P. Harrit, Unit Operatins f Chemical Engineering, 4th Ed., McGraw-Hill, New Yrk (1985) 2. Uhl, V.W., and J.B. Gray, Mixing, Thery, and Practice, Vl. 1, Academic Press, New Yrk (1966) p 164 Chemical Engineering Educatin