Modeling a Single-stage Hydrocyclone for Potato Starch. Separation

Transcription

1 1 Mdelng a Sngle-stage Hydrcyclne fr Ptat Starch Separatn L Shjn Ln Yalng hnese Academy f Agrcltral Mechanzatn Scences N.1 Beshatan, Deshengmen Wa Bejng, , HINA ssannacn@yah.cm.cn Abstract Data frm experments n separatn f ptat starch by a sngle stage hydrclne were analyzed based n smlarty thery. The stepwse regressn was then sed t establsh mathematcal mdels that best descrbed the effects f a sngle stage hydrclne n separatn f ptat starch. The mdels can be sed t predct the separatng perfrmance, and as a theretcal bass fr scalng-p desgn, parameter ptmzatn and ther applcatns. Many cmpanes arnd the wrld are sng hydrcyclnes fr starch separatn becase f ther smple desgn and peratn. Key wrds: Starch, hydrcyclne, mathematcal mdel 1Intrdctn The lteratre research shws that stdes n hydrcyclnes sed fr separatn f ptat starch have been cndcted nly n a few cntres ncldng Hlland, Pland, the Unted States and Rssa [1]. There s n evdence ndcatng that hna has been nvlved n ths feld f stdy. The flw f fld nsde a hydrcyclne s a cmplex prcess and there are many factrs nflencng the effcency f separatn. It s therefre necessary t have a thrgh nderstandng f the nflencng factrs and ther relatnshps t predct the separatng perfrmance f a hydrcyclne [,3]. Untl nw, few stdes n the nderflw cncentratn have been reprted n dcments cncernng the predctn mdel, althgh t has a sgnfcant nflence n the effcency f a separatn system [4]. In a separatn prcess, verflws are retrned t the prevs stage(s) as mther lqd. A t hgh r lw verflw cncentratn wll nt nly have mpacts n the chce f ts prevs hydrcyclne (s), bt als n the determnatn f separatn parameters. Hence, t s apprprate t develp mathematcal mdels fr nderflw cncentratn and verflw cncentratn [5~8]. In ths stdy, the crtera btaned by dmensnal methd fnd n smlarty therem were sed t flter expermental data [9]. A stepwse regressn mdel was develped n the fltered data wth mathematcal sftware, Matlab, t predct the perfrmances f hydrcyclne. S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

2 Separatn rtera Eqatn.1 Smlarty rtera Smlarty crtera (r smltde parameters) are dedced accrdng t A.O.φeepmaH's(Rssan langage) dmensnal analyss [9]. As the frst step, a dmensnal analyss s perfrmed n each f the parameters and perfrmance ndcatrs. Physcal parameters that have the same dmensns can be expressed as the rat f ne parameter s vale t anther. The resltng crtera are bvsly dmensnless and may be sed as smlarty crtera. Fr strctral parameters, we have 1 : 1 D/D where, D s the dameter f nderflw penng (mm); D s the dameter f verflw penng (mm). Fr physcal characterstc parameters, we have : where, s the starch cncentratn f nlet(%). Anther parameter that has sgnfcant nflence ver the perfrmance f separatn s the sld cntent g, let: 3 g / where, g s the sld cntent (%). N and N are tw addtnal dmensnless physcal parameters, and can be expressed as Let: 4 N 6 De/D 5 N 7 De/De where, refers t the nlet, the verflw and the nderflw. N and De are tw parameters n the nted Rsn-rammler eqatn [], standng fr the dstrbtns f partcle sze. De s a cnstant that s n drect prprtn wth X 50 (.e., a dameter f partcle belw whch the cmlatve dstrbtn f partcle sze amnts t 50 percent). N s determned by the range f partcle sze dstrbtn. The greater the vale f N, the smaller the range f partcle sze dstrbtn, shwng that the dstrbtn f sampled partcle sze s mre hmgenes. The ther crtera cncerned wth the separatng prperty s 8, let 8 n/1 Where, n s the nmber f hydrcyclne tbes n parallel wthn a cyclne. The peratng varables and are dented by: S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

3 Where, and are the starch cncentratn respectvely n verflw and nderflw (%). The separatn fnctn parameters dented by 11 S, 1 Et 1 and 13 Et are gven by: Et Et 1 ( g - g ) g ( g - g ) g G ( - ) G ( - ) 1 Where, S s the splt rat f nderflw vlme t verflw vlme; Et 1 s the separatn effcency f starch; Et s the verall effcency f separatn and; g and g are cncentratns f slds n verflw and nderflw respectvely (%). The remanng parameters nclde D, P, Q I,ρ andμ, n whch the smlarty crtera are gven by dmensn analyss methd. Amng them, D, P and ρ can be regarded as basc varables accrdng t Bckngham s therem [3], whch can then be ntegrated wth Q and μ respectvely t btan tw dmensnless qanttes. Then we have tw smltde parameters: 14 15,, µ ρ P D 8 ρ D Q P Where, μ s the vscsty f entrance materal (Pa S); where Pa s n Pascals, s s the tme n secnds, ρ s the densty f nlet materal (kg/m 3 ); P s the pressre f ncmng fld (Mpa) and; Q s the flw f nlet materal (m 3 /h). Let: µ P 5 ρ P D A crtera representng the changes n peratng pressre. The Eler nmber (E) E D P 4 8ρ Q 6 s Here, the Eler nmber (E) refers t the relatnshp between the drp n pressre and the prdctn capacty. As dmensnless varables wll reman dmensnless after any algebra r expnental peratn, then 14 and 15 can be smplfed nt the fllwng frms: 14 E 15 P All the abve smlarty crtera are re-srted n terms f settled crtera and pended crtera (table 1). It wll nt change the behavr f the sbseqent mdelng S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

4 4 after re-srtng. Table 1 Smlarty rtera N. rtera N. rtera N. rtera N. rtera 1 Π 1 D /D 5 Π 5 D e /D 9 Π 9 13 Π 13 S Π 6 Π 6 E 10 Π Π 14 Et 3 Π 3, / 7 Π 7 P 11 Π 11 N 15 Π 15 Et 1 4 Π 4 N 8 Π 8 n 1 Π 1 De /De. Separatn crtera eqatn The smlarty crtera may fall nt tw types: the settled and the pended. Thse wth knwn physcal vale n sngle varable cndtns are called settled smlarty crtera. In cntrast, the smlarty crtera wth nknwn physcal vale are called pended crtera. Of the abve smlarty crtera, Π1 thrgh Π8 are settled crtera. Frm the thrd smlarty therem, t s clear that the prereqste fr smlarty f physcal phenmenn s that the settled crtera mst be eqal. Fr pended crtera t be eqal, t s necessary that physcal phenmenn mst be eqal. Therefre, there exsts a casal relatnshp n natre between these tw types f crtera. Sch a relatnshp may be expressed as a nvalent fnctn r crtera eqatn. It can be seen frm the abve analyss that pended crtera Π9 thrgh Π15 can be expressed by a fnctn f settled crtera Π1 thrgh Π8 [9]. Based n past experence and engneerng practce, smltde parameter eqatn f vars knds can be descrbed n the frm f a pwer fnctn. In ths paper, the expermental data are Start fltered by sng smlarty crtera and analyzed wth Stepwse stepwse regressn methd. Read-n data The stepwse regressn s t select asscatve Dsplay reslt varables that have Determne parameters and the sgnfcant nflences ver nmber f samples Prnt the dependent varables n establshng regressn Data prcessng eqatns. Fr ths prpse, the mst sgnfcant End ndependent varable s alclate the crtcal always taken frm an ntal mdel and pt nt the Fg 1. The algrthm f stepwse regressn regressn mdel n an teratve way, n rder t test the ndependent varables cntaned n the rgnal mdel ne by ne. Insgnfcant varables are left t ntl n varables wll be entered nt n ne hand and left t frm the regressn eqatn n the ther hand. Fr the S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

5 5 basc algrthm, see fgre 1. Regressn analyss s dne n experment data wth Matlab. And then, F test s perfrmed n each f the parameters at a sgnfcance level f 5 percent. The parameters are accepted r rejected accrdng ther ranges f sgnfcance. The resltng mathematcal regressn mdels f smlarty crtera are as fllws D ' 0.08 E D D De. ( ) N D D ( N ) 1.13 ( ) N D 4. n D ( ) ( ) N E ( P ) ( ) De De D n D ( ) ( ) ( ) N E P ( ) S De.176 n D. 067 ( ) Et Εt ( ) ( ) N De D 3. Analyss f Mathematcal Mdels ( N ) ( E ) Accracy f Smlarty rtera As the F-test table shws when the sgnfcance level α0.05, the crtcal vale f F-test s: F F F F F Accrdng t the crrelatn ceffcent test table: When α0.05, the crrelatn ceffcents are: R , R 0.88, R 0.54, R ,5 89,4 89,3 89, Fr the statstcs f each mdel, see table S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

6 6 Table The statstcs f mdels Mdel S 1 R F P Relatve errr(%) N e De /De e S e Et e Et e It can be bserved frm table that the resdal sm f sqares (S) s very small fr each f the mdel and the relatve errrs are all wthn the range f acceptance. Mrever, mst f the crrelatn ceffcents (R) are abve 0.7, shwng that a gd ftness exsts between parameters and ndces. The vales f F are all greater than the crtcal vales gven by the test table, whch demnstrates that the mdels are sgnfcant at 95 percent level f cnfdence. The reslts calclated wth the mathematcal-mdels are gven n table 3 n cmparsn wth vales f measrements. It s bvs that predctrs calclated frm the regressn mdels have a hgh accracy. Table 3 Reslts calclated frm mathematcal mdels n cmparsn wth measrements N De/De S Et1 Et (E) (M) (E) (M) (E) (M) (E) (M) (E) (M) (E) (M) (E) (M) In the table, E dentes the measrement vale and M the vales calclated frm each mdel. 3. Dscssn 1 Mdel It can be seen frm Mdel that the verflw cncentratn () has a strng relatn wth the rat f nlet t tlet penng (D/D), the nlet starch cncentratn (), the cncentratn rat f nlet sld t starch, the nlet partcle sze dstrbtn, S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

7 7 and the nlet pressre. The rat f nlet t tlet penng, the nlet starch cncentratn and the dstrbtn f nlet partcle sze have hgher nflences than the cncentratn rat f nlet sld t starch. Mdel The mdel s determned by the rat f nlet t tlet penng, the nlet cncentratn f starch and the dstrbtn f nlet partcle sze. The dstrbtn f nlet partcle sze has the greatest mpact n the, whle the nlet cntent f starch has the smallest. 3 Mdel N Based n past experence, the smallest sze f partcle that can be separated may be rghly estmated accrdng t the dameter f a cyclne. Hwever, the applcablty f a cyclne fr a gven materal can be determned nt nly by ts separatn sze, bt als by the dstrbtns f partcle sze n materal befre and after separatn. They wll allw fr an verall nderstandng f the cyclne s applcable fr separatng a gven materal at relevant peratng cndtns. It s bserved frm the mdel that the dstrbtn f partcle sze and the rat f nlet t tlet penng have greater nflences than the nlet pressre, wrkng capacty and the nmber f hydrcyclne tbes cnnected n parallel. 4Mdel De/De The mdel has a smlar frm t Mdel N, and the parameters have smlar behavrs. 5Mdel S In the present practce, the calclatn f splt rat s based n an emprcal frmla whse scpe f applcatn s sally restrcted by the materal prpertes and the strctral parameters f a cyclne. In rder t prvde a mdel fr splt rat that best descrbes the separatn f ptat starch, an emprcal frmla s wrked t thrgh the abve regressn analyss. It s clear that the mdel s determned by the starch cntent and partcle sze dstrbtn f nlet materal and the nmber f hydrcyclne tbes wrkng n parallel at each separatn stage. 6 Mdel Et 1 As an mprtant ndcatr stded n ths research, the separatn effcency f starch represents the separatng perfrmance f hydrcyclne. Therefre, t s necessary that an accrate predctn f the separatng perfrmance shld be made t determne the strctral parameters and the peratng varables f a hydrcyclne. The mdel s largely determned by the dstrbtn f nlet partcle sze, and then by the wrkng capacty, peratng pressre and the starch cntent f nlet. 7 Mdel Et The separatn effcency f sld cntent s sed fr cmparsn n ths stdy, whch has strng relatnshps wth the partcle sze dstrbtn and starch cntent f nlet. It may be cnclded frm the abve dscssn that all the mdels are prmarly determned by the rat f tlet t nlet penng, the partcle sze dstrbtn f nlet, S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.

8 8 the starch cncentratn f nlet and the peratng pressre. It s therefre especally mprtant t reglate these fr parameters s as t btan an ptmal stats f separatn n real prdctn. 4. nclsn The mathematcal mdels develped n the bass f experments, nt nly allw fr a relable predctn f the perfrmance f a sngle stage hydrclne fr separatng ptat starch, bt als prvde an effectve way t test the desgn f hydrclne fr ptmal perfrmance [10]. The mdel can predct the reslt f separatn perfrmance. Ths t can redce the cst f experment and debggng. References 1 L Shjn, GaYan, and SnYn. Stdy n perfrmance f a mn-hydrcyclne fr ptat starch separatn. Transactns f the hnese Scety f Agrcltre Machnery. 001,3(6): Paper n hnese. Qjashan. Research n the experment and smlatn f the hydrcyclne and flter prcessng f the clsed crcle system dealng wth phsphrc acd sewage. Master s degree paper. hengd Scence and Technlgy Unversty Paper n hnese. 3 Wllams, R.D. The se f hydrcyclnes fr small partcle separatn. Separatn Scence and Technlgy. 1983,N18: Paper n Englsh. 4 Zh Langyn, hen Wenme, and Da Ganqng. Hydrcyclnes. Bejng:hemstry Indstry Pblshng Hse,1998. Bk n hnese. 5 Rldan Vllasana, E.J., T. Dyakwsk, M.S. Lee, F.J. Dckn, and R.A. Wllams. Desgn and mdellng f hydrcyclne and hydrcyclne netwrks fr fne partcle prcessng. Mnerals Engneerng 1993,6(1): Paper n Englsh. 6 Wllams, R.A., Albarran de Garca, I.L. ln, M.S. Lee, and E.J. Rldan Vllasana. Desgn targetng f hydrcyclne netwrk. Mnerals Engneerng 1994,7(5/6): Paper n Englsh. 7 Rldan Vllasana, E.J., and R.A. Wllams. alclatn f a steady state mass balance fr cmplex hydrcyclne netwrks Mnerals Engneerng. 1991, 4(3/4): Paper n Englsh. 8 Schwalbach, W.W. Three smple steps t hydrcyclne selectn. Fltratn and Separatn. 1988, 5(4):64-66.Paper n Englsh. 9 L Zhgang. Smlarty and Mdelng. Natnal Defense Indstry Pblshng Hse Bk n hnese. 10 Lagtkn, M.G., and D.A. Barannv. Selectn f ptmal and regme parameters fr the peratn f hydrcyclnes. hemcal and Petrlem Engneerng. 1998,34(1):79-8. Paper n Englsh. S. L and Y. Ln. Mdelng a Sngle-Stage Hydrcyclne fr Ptat Starch Separatn. Agrcltral Engneerng Internatnal: the IGR Jrnal f Scentfc Research and Develpment. Manscrpt FP Febrary, 004.