IDENTIFICATION OF RHEOLOGICAL DEPENDENCIES OF OIL MATERIAL PROCESSED IN A SCREW PRESS

Internationa Journa of Mecanica Engineering and Tecnoog (IJMET) Voume 8, Issue 10, October 017,. 708 718, Artice ID: IJMET_08_10_077 Avaiabe onine at tt://www.iaeme.com/ijmet/issues.as?jteijmet&vte8&ite10 ISSN Print: 0976-630 and ISSN Onine: 0976-6359 IAEME Pubication Scous Indexed IDENTIFICATION OF RHEOLOGICAL DEPENDENCIES OF OIL MATERIAL PROCESSED IN A SCREW PRESS Aexander V. Gukasan Kuban State Tecnoogica Universit,, Moscovskaa St., Krasnodar, Krasnodarskij kraj, 35007, Russia ABSTRACT In te resent work it as been found tat te voume fow rate of structured fuid, defined for Bingam astic troug an exaust device of a ress, is rigid core fow. Wit tat, te strain in tis does not exceed te ied oint of a Bingam astic. An equation as been obtained tat generaizes te known one-dimensiona Poiseuie equation, wic aows to determine functiona deendenc of voume fow rate of a structured Bingam astic troug te discarge device of te ress, wic significant increases te accurac of identifing reoogica indicators of te fow wit known geometric arameters of te outet device. Kewords: aered stead fow; Heaviside ste function; ied oint; astic viscosit. Cite tis Artice: Aexander V. Gukasan, Identification of Reoogica Deendencies of Oi Materia Processed In a Screw Press, Internationa Journa of Mecanica Engineering and Tecnoog 8(10), 017,. 708 718. tt://www.iaeme.com/ijmet/issues.as?jteijmet&vte8&ite10 1. INTRODUCTION Oi-bearing materia is ressed in singe-rotor screw resses [1]. Wen a screw wit variabe geometr of cois tat reduce te free voume of fied oi-bearing materia is rotating, ressure occurs, wic transorts te materia, and oi is ressed troug te gas between moder stras combined into a moder cinder tat covers te screw saft []. Fitering of oi troug astica deformed orous mixture and extraction of oi to te outside of te canne of te extruder troug a moder camber cause radia ressure dro in te oi [3]. Te materia in te canne of te rotating screw tat is imited b te stationar ousing wi start moving steadi troug te canne due to te sear strain tat occurs in it te forced (straigt) stream aears. Te main arameters tat determine te voume fow [] are canne det and widt, screw diameter, and frequenc of rotation. Te condition for return fow occurrence is te excessive ressure created b ead resistance. Te overa erformance of te screw comressor is te sum of fow rates. Tus, erformance of screw resses is determined b interaction of te suercarger and te forming ead (cone) troug te moder extraction tat determines te voumetric fow rate of te materia entering te forming tt://www.iaeme.com/ijmet/index.as 708 editor@iaeme.com

Identification of Reoogica Deendencies of Oi Materia Processed In a Screw Press ead. In te first aroximation, we anaze tree s of te ress. Te first one is te comressor, wic is te of te feed screw [5]. Te second one is te of ressing, wic ma be reresented b a rectanguar cross-section canne tat narrows wit eigt and widt [6], and is adjacent to te ead, wic is regarded as te tird zone of te extruder, being a combination of a cindrica and a conica canne wit variabe geometr [7]. Te existing modes of fitering fuids troug non-deformabe orous media [8] and te modes of fitering in eastic deformabe environments [9] do not aow modeing te fow of te viscous-astic non-newtonian fuid comicated wit te rocesses of comressibiit, diffusion and mass transfer in te existing industria instaations. Tis work is aimed at determining functiona deendence of te arameters of te voumetric fow matematica mode in te fow of viscous-astic medium in ressing oi during extrusion of oi cutures in a roduction instaation.. METHODS Identification of materia fow in a screw extruder is based on reverse motion tat is simiar to te Couette fow robem (te screw is stationar, and te bod is rotating). In tis case, te screw canne unfods onto te ane, and te ongitudina section srands out, te ower border of wic remains stationar, wie te uer section is moving wit secified seed. Te eigt of tis canne H corresonds to te cutting det of te feed screw, and engt L corresonds to te engt of te generatrix of te eix. Te second zone corresonds to te cubic sine aroximation of te cross section of moder cois in te beginning, in te midde and in te end of te cutting det of eac of tese cois. It ma be reresented in a simified form as a ressing zone tat is narrowing wit eigt. Tis is adjacent to te ead tat is regarded as te tird zone of te extruder, wic is a combination of a cindrica and a conica canne wit variabe geometr. Taking into account te ratio of tese cannes' engts of a rea roduction ress [10], tis ma be reresented as a fat Poiseuie fow. Te extruded materia tat asses te moder zone is two-comonent viscous-astic non- Newtonian fuid tat consists of fibers tat form a orous structure, and Newtonian fuid (oi) distributed witin its ores [11]. Densities of te fibers and oi do not cange, but wen oi is ressed in te moder, tis sstem sows comressibiit associated wit te fitering roerties of te mixture. In tis case, te cake as te roe of te orous skeeton saturated wit oi. During ressing, te working is considered comete fied wit te mixture. Te ressing rocess is considered isoterma [1]. Sma seeds determine te mixture fow as aminar for describing te saturated fuid of te orous medium. Cake of te oi cuture serves as te first ase, te second ase is oi [13]. Movement of te materia troug te first and te tird zones of te ress is modeed as reoogica fow defined b sear rate, (Pa) containing two coefficients: ied oint - T (Pa) and astic viscosit (PA sec), combined in fow equation [1] for Bingam structured fuids: & γ (1) Were γ& is te sear rate, (Hz). Tus, in te first aroximation, te fow of materia in te first and te tird zone of te extruder ma be reresented b aered fow were te veocit comonent of one of te coordinate ines is not equa to zero [15]. In te Cartesian coordinate sstemv U 0, v 0, v 0. Terefore, from te continuit equation x z U(, z t). In tis case, from te Navier Stokes equation it foows tat ( x, t ) U,. Tese ratios determine te stationar Poiseuie - Couette aered fow in te first zone, and te stationar aered Poiseuie fow in te tird zone of te extruder. Te materia of te tt://www.iaeme.com/ijmet/index.as 709 editor@iaeme.com

Aexander V. Gukasan ases is incomressibe. In tis case, densities of te comonents remain uncanged, but te voumetric densities cange during te rocess of ressing. Te Poiseuie aered stead fow in te tird zone of te extruder is determined b ( x) U(, z) U(, z) equation µ. Te rigt side of te equation does not deend x z ( x) ( x) on variabe x. Terefore, 0, from were Const. In tis case, for te x x stead-state fow, were is canne engt in te tird zone of te extruder; Δ is te ressure difference at te boundaries of te zone. For Bingam astic, reoogica d equation wit regard to γ& U( ) ma be converted to te one-dimensiona stead-state d fow defined b equation: d U( ) d () Using te Laace transform, C L s 0 s s, we get te soution C of L differentia equation Error! Reference source not 3 s s s found.wit regard to integration constant C: U( ) C (3) In a viscous fuid sear stresses in te centra ane of te fow are equa to zero. Terefore, aminar core wi be formed cose to tis ane, were. Te strain inside tis wi be ure eastic, and it wi move as a rigid woe. Wit, we ave d U( ) 0. Terefore, for o, atoug tere is movement, fow is missing. Te afwidt of tis is determined b d equation: d C 0 d 0 () From equation, O. Tus, te fow in te tird zone of te extruder is a rigid core fow wit af-widt o determined b equait O. Te strain in tis zone does not exceed te ied oint. To determine te seed of a ard ate, from equation we define C, assuming tat siage of te materia is absent on te was of te examined zone ± ( is af-eigt of te canne). In tis case, te integration constant C of equation is determined b equation: C (5) tt://www.iaeme.com/ijmet/index.as 710 editor@iaeme.com

Identification of Reoogica Deendencies of Oi Materia Processed In a Screw Press tt://www.iaeme.com/ijmet/index.as 711 editor@iaeme.com Te seed of rigid cinder v o wit af-tickness o is found b substitution of O in equation given tat: ( ) v 0 (6) Te fow rate of viscous materia in te zone adjajcent to te was of te canne is determined b formua: ( ) ( ) ( ) v (7) Te overa fow rate of te materia in te tird zone of te canne tat is defined b formuas and ma be reresented b generaized reationsi: ( ) ( ) F F U 8 (8) Were F() is a Heaviside ste function. Graica, tis deendence is a iecewise continuous function (Figure 1). Figure 1 Deendence of fow seed (U) on its eigt (). Integration of formua Error! Reference source not found. b te of canne aows to determine te voumetric fow rate of structured fuid troug te discarge device of te ress: ( ) ( ) ( ) ( ) b d U b Q b 0 3,,,,, (9) Te voumetric fow rate defined b equation generaizes te we-known onedimensiona Poiseuie equation wit 0. Te use of formua aows to secif functiona deendence of te voumetric fow rate of a structured Bingam astic troug te discarge device of te ress, wic significant increases its accurac [16].

Aexander V. Gukasan 3. RESULTS AND DISCUSSION To identif te reoogica fow indicators incuded in equation wit te known geometric arameters of te discarge device, et us consider te inearized variant of te ressing rocess, wic is caracterized b te foowing basic geometrica arameters (Tabe 1). Tabe 1 Basic geometric arameters of te ress No. Coi Diameter bade coi det ste engt of te mouder of te saft bottom to eigt 0 6.5 90 60 50 1 3 6.5 1 6.5 35 10 50 1 30 0 6.5 6.5 155 170 50 1 15 6.5 3 37.5 130 15 00 1 3 13 37.5 31.5 115 10 00 13 1 13 31.5 5 0.5 110 135 0 17 0 1 0.5 6 16.5 100 135 0 18 0 1 16.5 7 16.5 8 100 0 0 0 1 16.5 i H B, S B, L B, D З, D B, a, b,, Considering te inearized tree-zone mode of te ress, cacuation of te geometrica caracteristics of tese zones (Tabe ) was made. Tabe Linearized geometric arameters of tree zones of te ress Press zone coi det coi widt engt aong te eix comressor 6.5 71.6 7.7 ressing zone at te intake 6.5 71.6 at discarge 1. 83.5 5,733.8 π 107.9 10 107. ead (average) 1. ( ) unit of meas. Te use of te inearized mode geometr (Tabe ) aows identifing te boundar conditions of te centra extraction zones of te comressor (te ane-arae Couette fow) [17] and te discarge device (ane-arae Poiseuie fow) were oi extraction is absent. Te data are resented in te form of five exeriments (Tabe 3). Tabe 3 Test data No. L N t M F c 0 7.6 1.571 87 1,57 16.65 1 9.09 89 1,831 16.8 9.87 88 1,868 19.9 3 10.5.87 89,08 1.8 1.1.87 88,06. Meas. Hz o C kg/our % Designations X 1 X X 3 Y 1 Y Exeriments aimed at identifing arameters of te matematica mode tat describes te oeration of te screw ress (Tabe ) were erformed at four eves of te ress discarge device trougut caacit (te widt of te outut sit L, ); tree eves of screw rm (N, Hz) and tree eves of temerature (t, o C). Te resented data (Tabe 3) sow tat tis tt://www.iaeme.com/ijmet/index.as 71 editor@iaeme.com

Identification of Reoogica Deendencies of Oi Materia Processed In a Screw Press resuted in te canged screw ress trougut erformance (M, kg/), and te residua oi content in te cake (Fc, %). We sa consider te isoterma task witout te energ equation (temerature is conventiona considered as constant vaue). Given te nature of te materia, we sa consider it virtua incomressibe te densit of te comonents (oi and fiber) is constant. Let us consider canges of te mas in te rocess of ressing. Let's assume tat its densit in te beginning of ressing (masing) is equa to (1,0501,50)/1,150 kg/m 3. Tis densit is determined b equation: F in oi ( 1 F In ) materia mas in (10) Were F in 50% is te initia oi content. Ten te materia densit according to equation is equa to 1,9 kg/m 3. In tis case, fina densit is determined b equation: F c oi ( 1 F c ) materia (11) were F is fina oi content determined according to te exerimenta data. Wit regard to te data of equation, we get mas densit on te cone of te ress. Considering incomressibiit of oi and materia in te rocess of ressing, we find te voume of te mas at te entrance to te ress b te foowing ratio: M kg in F in 871 m 3 Tus, materia densit is determined b equation: f 1,9 558 f ( m ) m ρ c kg ( 1 F in )19 Q in m 3 (1) ρ m (13) Were f m is oi content in te materia in te rocess of ressing, kg/kg. Let us use te obtained data for cacuating te deendence of te mas densit on its oi content. Anasis of te exerimenta data sows te ossibiit of using inear aroximation of deendence of te desired mas densit on oi concentration in it [18]. Knowing te reduction in te oi content (Tabe ) in te rocess of ressing, and oi densit, et us determine fow rate of te mas wit regard to equation at te exit from te ress b te difference between tese fow rates (Tabe ). Tus, te fow rates at te exit from te ress were obtained in te exeriment. Data anasis (Tabe ) sowed tat te trougut caacit of te ress deended on te geometr of te forming bod, and on te screw rotation seed [19]. Tabe Voumetric fow rate of te ress Exerimenta data Mas densit in te cone Mas fow rate at te entrance No. 1 3 5 Meas. M init 1,57 1,831 1,868,08,06 kg/our N v 1.571.09.87.87.87 Hz t 87 89 88 89 88 o C δ 7.6 9 9 10.5 1.1 F c 16.65 16.8 19.9 1.8. % ρ c 1,336 1,335 1,318 1,310 1,30 kg/m 3 Q init 1,67 1,59 1,6 1,763 1,795 iters/our tt://www.iaeme.com/ijmet/index.as 713 editor@iaeme.com

Aexander V. Gukasan to te ress Mas fow rate at te exit from te ress Q c 709 89 980 1,095 1,11 iters/our Terefore, one can make a concusion about te Bingam fow of te materia at te discarge device of te ress [0]. Oterwise, te trougut caacit wi be determined on b te geometr of cois, wic contradicts te exerimenta data. To determine te sares of tese currents, te data were anazed wit regard to te of te annuar ga, wic was canged during te exeriments. Tabe 5 Test data wit regard to te canges in te of te outut device of te ress (δ ) and te Bingam fow in te annuar ga No. M init N t δ δ F c M end Paraboa Piston ΔS 1 1,57 1.571 87 7.6 57.76 16.65 85 36 67% 159 33% 1,831.09 89 9 81 16.8 615 397 6% 3 36% 3 1,868.87 88 9 81 19.9 75 5 70% 3 30%,08.87 89 10.5 110.5 1.8 863 5 63% 303 37% 5,06.87 88 1.1 16.1. 95 5 56% 0 % meas. kg/our Hz o C % kg/our kg/our % kg/our % Statistica anasis of te data (Tabe ) sowed tat wit te reiabiit of 95%, te deendence of initia erformance on te reoogica erformance of te ress was described b te foowing reationsi: M a1n ( N; δ ) a e b δ init 0 0 (1) a 0 181 kg/; a 1 0.37 sec; b 0.78 kg/(our ). Wit tat, te reative error of tis deendence is 1%. Considering te additive nature of te obtained regression reationsi, one can estimate te contribution of te araboic and te iston fow. Tis concusion es exain te additive nature of te obtained regression equation, te first suand of wic corresonds to erfect astic fow (araboic rofie) and second one - to te sift (iston) fow of astic materia exiting te ress. Besides, tis equation ma be used for first aroximation assessing te contribution of tese currents b taking te estimated erformance as 100%, and te resective suands as sares of te resective fows (Tabe 5). As one can see from te sown data, te sare of iston fow increases wit increased roductivit (from 33% to %), wic confirms te nature of te Bingam fow in te annuar ga of te discarge device of te ress. Te considerabe deendence of te accurac of describing te exerimenta data on rotation seed and te ga sows redundanc of te studied number of factors in te exeriment, name, te temerature variation in te exeriments ma be negected. Let us consider te Bingam fow in te annuar ga of te discarge device between te coaxia fixed cinders witout siing, reative to te canne was. Te canne engt wi be determined based on te trougut caacit of te discarge device. Tis device incudes a coaxia cindrica and a narrowing conica cannes, te geometr of wic varied during te ress arameters identification exeriments (Tabe 6) [1]. tt://www.iaeme.com/ijmet/index.as 71 editor@iaeme.com

Identification of Reoogica Deendencies of Oi Materia Processed In a Screw Press Geometrica arameters of te fow at te exit Tabe 6 Geometrica arameters of te die (cone) of te ress No. of exeriment 1 3 5 meas. cinder cone R i 107.818 107.818 107.818 107.818 107.818 R o 10 10 10 10 10 L с 67.1 79.59 79.59 9.85 107 r e 107.9 107.9 107.9 107.9 107.9 r 1e 10 10 10 10 10 r 1a 11. 111.0 111.0 109.5 107.9 r a 10 10 10 10 10 L c 39.79 7.1 7.1 1.15 1 Movement of te materia in tis zone of te ress is modeed as reoogica fow defined b sear rate, (Pa) containing two coefficient: ied oint - T (Pa) and astic viscosit (PA sec), combined in fow equation for Bingam structured fuids. Te overa fow rate of te materia in te tird zone of te canne defined b formuas and ma be reresented b generaized reationsi. Substituting, one can convert into a more convenient O form, integration of wic over te of canne b aows to determine te fow rate of structured fuid troug te discarge device of te ress: с,,, Φ Φ т Were γ is te coefficient tat is roortiona to te materia sear rate in te die. Te voumetric fow rate defined b equation generaizes te we-known one-dimensiona Poiseuie equation wit T 0. Te use of formua aows to determine functiona deendenc of te voume fow rate of structured Bingam astic troug te discarge device of te ress, wic significant increases te accurac of identifing reoogica indicators of te fow wit te known geometric arameters of te outet device (Tabe 6). In te zone of iston fow wit radii a, b (R 1 <a<b<r ) (were R 1, R are te radii of coaxia cinders), te materia moves astica, wie outside of tis section te fow is viscous. Given te fact tat te curvature of te circuar canne does not exceed 1%, we beieve tat te geometr of te structured fuid astic fow troug te discarge device of te ress (ab) is determined b deendence. Te overa fow rate at given ressure dro Δ is defined as te sum of te fow rates of te tree annuar sections. Using functiona deendence, it was ossibe to т igigt reoogica arameters γ reative to sear rate coefficient (γ). Soution wit R1 R regard to te of existence of soution 0 0 R1 aows to determine te fow rate in te tird zone of te ress as a function of af-widt of tis zone ( 0 ) to te sear rate coefficient (γ). Combining te sstem of equations tat conbines te geometr of te astic fow canne wit te voumetric fow rate of te discarge device, we get an equation for identifing arameters of af-widt of te rigid core zone in te centra art ( 0 ), and te coefficient of sear rate (γ): (1) tt://www.iaeme.com/ijmet/index.as 715 editor@iaeme.com

Aexander V. Gukasan с!,, "",# $% & ' & с!,, * "",# $% & *' &*,,,,, с!,, ) "",# $% & )' &) с!,, "",# $% & ' & с!,, "",# $% & ' & Were i is af-widt of te rigid core zone; i is te number of te identified exeriment, i0,1,..., (Tabe ). Te minimum of target function defines te geometr of te astic core and te reoogica roerties of te fow wit regard to te existence of a soution of equation set b te foowing sstem of inequaities: 0 0 ( ) R 1 meanr 1, R meanr 1, R meanr 1, R meanr 1, R 0 1 0 0 3 0 (17) Te resut of minimization wit regard to constraints sows te resence of a astic core, te tickness of wic decreases wit increasing trougut caacit of te ress (Tabe 7). Tabe 7 Identification of reoogica arameters of te ress die oeration No. 1 3 5 Meas. Exerimenta data M init 1,57 1,831 1,868,08,06 kg/our Mas densit in te cone ρ c 1,336 1,335 1,318 1,310 1,30 kg/m 3 Mas fow rate at te exit from te ress Q c 709 89 980 1,095 1,11 iters/our Haf-widt of te rigid core zone 0 1.716 1.8 1.397 1.95 1.58 Sear rate coefficient γ 5.35 Hz. CONCLUSION As a resut of exerimenta data identification according to te Bingam mode of viscoastic fow, te resence of a rigid core witout sear strains as been estabised. Wit increasing materia fow troug te discarge device of te ress, te rigid core zone decreases. In a exeriments, te sear rate coefficient in te aminar fow zone adjacent to te was of te discarge device remained constant. Tus, te ressure deveoed b te ress exceeds te ressure of astic fow. Te identified fow modes are to be considered in deveoment of te rocesses imited b aminar fow modes in mutiase sstems. REFERENCES ( ) R 1 ( ) R 1 ( ) R 1 [1] Kosevo, E. P., Kosacev, V. S. and Garus, A. A. Otzim zidkoi fazi iz disersnogo materiaa s eremennoi naororovodnostu [Pressing te iquid ase of disersed materia wit variabe ressure conductivit]. In coection: Innovative food tecnoogies in te of storing and rocessing agricutura raw materias Materias of te Internationa scientific-ractica conference. Under te genera editorsi of R. I. Sazzo. 011,. 6-31. [] Meretukov, Z. A., Kosacev, V. S. and Kosevo, E. P. Resenie zadaci neineinoi naororovodnosti ri otzime [Soving te robem of noninear ressure conductivit in ressing]. News of iger educationa institutions. Food tecnoog, 5-6 (33-3), 011,. 6-6. [3] Gukasan, A. V., Kosevo, E. P. and Kosacev, V. S. Tecenie masicnogo materiaa v viusknom ustroistve [Oi materia fow in te discarge device]. In coection: Penomena of transfer in te rocesses and aaratuses of cemica and food roduction. Materias of te II Internationa scientific-ractica conference, 016,. 16-150. (16) meanr ( 1, R ) R 1 tt://www.iaeme.com/ijmet/index.as 716 editor@iaeme.com

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Aexander V. Gukasan [0] Gra, G. R., Dare, H.C.H. Comosition and roerties of oi we driing fuids. Moscow: Nedra, 1985, 509. [1] Gukasan, A.V., Kosevo, E.P. and Kosacev, V.S. Ustanovka da CO ekstraktsii tverdo- i zidkofazni smese [Instaation for CO extraction of soid- and iquid-ase mixtures]. In coection: Food industr: integration of science, education and roduction Materias of te A-Russian scientific-ractica conference wit internationa articiants, 005,. 16-165. [] Lacen Safraoui, Basma Benadou, Abdea Haddout, Mariam Benadou and Fatia Rric, Infuence of Twin Screw Configuration on te Disersion Quait of te Hig Concentration Coored-Masterbatc. Internationa Journa of Mecanica Engineering and Tecnoog, 8(), 017,. 66 76. [3] G. Prasanna Kumar, N. Seetaramaia and B. Durga Prasad, Investigation of Magneto- Reoogica Fuid (MRF) Boring Bar For Catter Stabiit. Internationa Journa of Mecanica Engineering and Tecnoog, 7(), 016,. 175 18. [] N. P. Serje and Dr. S. V. Desmuk, Prearation and Caracterization of Magnetoreoogica Fuid For Damer In Automobie Susension. Internationa Journa of Mecanica Engineering and Tecnoog, 7(), 016,. 75 8. [5] M. Raju, N. Seetaramaia, A.M.K. Prasad and M.A. Raman, Exerimenta Anasis of Magneto-Reoogica Fuid (MRF) Damers under Trianguar Excitation. Internationa Journa of Mecanica Engineering and Tecnoog, 7(6), 016,. 8 95. tt://www.iaeme.com/ijmet/index.as 718 editor@iaeme.com