Performance Analysis and Improvement of Flat Torque Converters Using DOE Method

Transcription

1 Chins Journal of Mchanical Enginring ORIGINAL ARTICLE Opn Accss Prformanc Analysis and Improvmnt of Flat Torqu Convrtrs Using DOE Mthod Guang Qiang Wu 1,2*, Ji Chn 1 and Wn Ji Zhu 1 Abstract Automotiv torqu convrtrs hav rcntly bn dsignd with an incrasingly narrowr profil for th purpos of achiving a smallr axial siz and rducing wight. Dsign of xprimnt (DOE) and computational fluid dynamics (CFD) tchniqus ar applid to improv th prformanc of a flat torqu convrtr. Four torqu convrtrs with diffrnt flatnss ratios (0.204, 0.186, 0.172, and 0.18) ar dsignd and simulatd first to invstigat th ffcts of flatnss ratio on thir ovrall prformanc, including fficincy, torqu ratio, and impllr torqu factor. Th simulation rsults show that th ovrall prformanc tnds to dtriorat as th flatnss ratio dcrass. Thn a paramtric study covring six gomtric paramtrs, namly, inlt and outlt angls of impllr, turbin, and stator is carrid out. Th rsults dmonstrat that th inlt and outlt angls play an important rol in dtrmining th prformanc charactristics of a torqu convrtr. Furthrmor, th rlativ importanc of th six dsign paramtrs is invstigatd using DOE mthod for ach rspons (stall torqu ratio and pak fficincy). Th turbin outlt angl is found to xrt th gratst influnc on both rsponss. Aftr DOE analysis, an optimizd dsign for th flat torqu convrtr gomtry is obtaind. Compard to th convntional product, th width of th optimizd flat torqu convrtr torus is rducd by about 20% whil th valus of stall torqu ratio and pak fficincy ar only dcrasd by 0.4% and 1.7%, rspctivly. Th proposd nw optimization stratgy basd on DOE mthod togthr with dsirability function approach can b usd for prformanc nhancmnt in th dsign procss of flat torqu convrtrs. Kywords: Torqu convrtr, Flatnss ratio, Computational fluid dynamics (CFD), Paramtric study, Dsign of xprimnt (DOE) 1 Introduction Torqu convrtrs ar an important part of automatic transmissions in automobils and othr vhicls. It provids automatic torqu amplification according to th diffrnt rotational spd btwn th input and output spds without any activ control, inhrntly supprssing ngin torqu fluctuations. Bcaus it significantly affcts th ful conomy, launch fling and drivability, intrsts in th dvlopmnt of a high fficincy and prformanc hav bn incrasd rcntly. In rcnt yars, with th dvlopmnt of computr tchnology, computational fluid dynamics (CFD) has bn widly usd in hydraulic machin dsign and optimization. Zhao t al. [1] optimizd a doubl-channl *Corrspondnc: wuguangqiang@tongji.du.cn 1 School of Automotiv Studis, Tongji Univrsity, Shanghai 2014, China Full list of author information is availabl at th nd of th articl pump s impllr by combind using of CFD, multiobjctiv gntic algorithm (MOGA) and artificial nural ntworks (ANN). Li t al. [2] carrid out an ntropy production analysis to invstigat th hump charactristics of a pump turbin basd on CFD simulations. Shojafard t al. [3], Tan t al. [4] studid ffcts of som gomtric paramtrs on fluid dynamic charactristics of a cntrifugal pump by CFD. Many rsarchrs hav also studid th flows in torqu convrtrs by using CFD cods mploying various mthods [, 6]. Sinc a numbr of variabls ar involvd in th dsign of a torqu convrtr, it is vry difficult to achiv an optimal dsign. In ordr to improv th convrtr prformanc, it is rquird to obtain dtaild undrstanding and rlationship btwn th govrning paramtr and its ffct on th prformanc, including fficincy, torqu ratio and impllr torqu factor. Kubo t al. [7] dscribd th rlationship btwn th dsign paramtrs usd to dfin Th Author(s) This articl is distributd undr th trms of th Crativ Commons Attribution 4.0 Intrnational Licns ( ivco mmons.org/licn ss/by/4.0/), which prmits unrstrictd us, distribution, and rproduction in any mdium, providd you giv appropriat crdit to th original author(s) and th sourc, provid a link to th Crativ Commons licns, and indicat if changs wr mad.

2 Pag 2 of 9 th gomtry of an automotiv torqu convrtr and th rsultant fficincy in rlation to th intrnal flow charactristics. Shin t al. [8, 9] invstigatd th ffct of ractor blad gomtry with varying thicknss ratios, scroll angls and slot angls on th prformanc of a torqu convrtr. Song t al. [10] prsntd an intgratd dsign procss TDOS (Torqu convrtr Dsign Optimization Systm) including torqu convrtr gomtry dsignr, 3D CFD analysis modul, and dsign optimizr. Th systm was usd to invstigat th ffct of dsign paramtrs on th prformanc. Most passngr cars with small and mdium siz ngins hav adoptd a front-whl-driv layout in rcnt yars. Torqu convrtrs accordingly hav bn dsignd with an incrasingly narrowr profil for th purpos of achiving a smallr axial siz and rducing wight. A numbr of rsarchrs hav studid th flat torqu convrtr mploying both analytical and xprimntal mthods. Ejiri t al. [11] manufacturd and tstd four torqu convrtrs with diffrnt flatnss ratios. Th xprimntal rsults show that th ovrall prformanc dtriorats whn th flatnss ratio is rducd to lss than about 0.2. Kim t al. [12] invstigatd ffcts of th stator with two diffrnt shaps suitabl for an axially squashd torus on hydraulic prformanc variation. Ochi t al. [13], Kitlinski t al. [14], and Usui t al. [1] dvlopd nw supr-flat torqu convrtrs to provid fr spac for nw quipmnts without much dprciation of fficincy. Ab t al. [16] mployd nwly dvlopd stator blads to dvlop th fluid flow channls for a thin typ torqu convrtr with a flattning ratio of 0%, whil maintaining torqu convrtr prformanc. Yan t al. [17] proposd a flxibl flat torqu convrtr and stimatd th influnc of th flatnss ratio on prformanc. Liu t al. [18] invstigatd th intrnal flow charactristics of th flat torqu convrtr basd on lliptical dsign path. Howvr, thr ar no rports rgarding combination ffct of th blad gomtry including inlt and outlt angls of impllr, turbin, and stator on th flat torqu convrtr prformanc charactristics. DOE mthod is widly usd to find th importanc lvl of th dsign paramtrs with rspct to th optimization targt and obtain th bst combination of dsign variabls. Park t al. [19] studid a mthan-fuld gas ngin gnrator with addition of hydrogn using DOE mthod. Hatami t al. [20] applid cntral composit dsign basd on DOE to obtain an optimal dsign of th van gomtry for a variabl gomtry turbin. Taghavifar t al. [21] applid DOE valuation to introduc th optimum injction stratgy-chambr gomtry of disl ngin. Howvr, thr hav bn rlativly fw applications of DOE mthod to flat torqu convrtrs optimization. In this papr, th main objctiv is to improv th ovrall prformanc of a flat torqu convrtr by using DOE mthod and CFD calculations. Firstly, prformanc charactristics of four torqu convrtrs with diffrnt flatnss ratios ar invstigatd. Thn, th snsitivity analysis is usd to analyz th influnc of inlt and outlt angls of impllr, turbin, and stator on th prformanc of a flat torqu convrtr. Finally, th optimization analysis is prformd by using DOE post-procssing analysis togthr with dsirability function approach. 2 Flat Torqu Convrtr Dsign 2.1 Torus Dsign Th flat torqu convrtr dsign startd with th dfinition of th torus shap. A torqu convrtr with 20 mm nominal diamtr was chosn as th prototyp modl. Elliptical dsign mthod was usd to rdsign th man stramlin of th torqu convrtr and flatnss ratio was rdfind as th rat of major axis and minor axis. Th rdfind flatnss ratio is rprsntd by th symbol in this papr. Givn th flow ara in th circular path, in th proposd torqu convrtr modl, was assumd constant, th shll and th cor shaps wr also rdsignd. Th torus dsign rsult compard with prototyp modl torus is shown in Figur 1. As shown in Figur 1, th rdsignd torus shows good agrmnt with th prototyp modl torus so that it could b usd to dsign flat torqu convrtrs. Four torqu convrtrs with diffrnt flatnss ratios wr dsignd and rfrrd to hr as typ 1 to typ 4, in dcrasing ordr of flatnss ratio, as shown in Tabl 1. Figur 1 Comparison of rdsignd torus with prototyp modl torus

3 Pag 3 of 9 Tabl 1 Paramtrs of torus with diffrnt flatnss ratios Paramtrs Typ 1 Typ 2 Typ 3 Typ 4 Nominal diamtr D (mm) Width of torus W (mm) Flatnss ratio Rdfind flatnss ratio Figur 2 illustrats th approach to shortn th axial dimnsion of th fluid flow channl. Th torus could b flattnd without changing th inlt radius R 1, and outlt radius R 2 of ach blad lmnt. Th dsign paramtrs wr unchangd as much as possibl xcpt th flatnss ratio and th stator axial lngth was proportional to th torqu convrtr axial lngth. In this prsnt papr, four typs of torus with diffrnt flatnss ratio ar dsignd using th sam mthod. 2.2 Blad Dsign Th impllr and turbin blads wr dsignd to match th flat torus without changing in thir inlt and outlt angls on th dsign path, a curv that biscts th flow passag cross-sctional ara. Th impllr had 31 blads and th turbin had 29 blads, which all had th thicknss of 1.0 mm. Th blads of four diffrnt stators all had th sam distribution of thicknss, it faturs rlativly thick profil, which was bttr hydraulic prformanc than thin blads. Thy wr also idntical to ach othr inlt and outlt angl xcpt for shaps. Th inlt and outlt angls on th dsign path for th thr lmnts ar shown in Tabl 2. Tabl 2 Inlt and outlt angls of thr lmnts Paramtrs Impllr Turbin Stator Inlt angl β 1 ( ) Outlt angl β 2 ( ) Flat Torqu Convrtr Dsign 3.1 Computational Mthod To rprsnt th complx gomtry of a torqu convrtr and gnrat th computational msh in an appropriat way, ICEM and Pro/Enginr rspctivly, wr usd. Th computational msh is givn in Figur 3 whr on blad passag is shown for ach lmnt to illustrat th msh distribution in th computational fild whn about 81,000 grid clls in total wr usd. Th lakag btwn th lmnts and also btwn an lmnt and th cor flow wr disrgardd. A cyclic boundary condition was imposd on both priphral boundaris outsid a blad passag. A no-slip wall boundary condition was also imposd on all th walls bounding th domain, with a spin applid as ncssary. Th intrfacs btwn lmnts hav bn handld by using th xplicit multipl rfrnc fram (MRF) mthod which allows th problm to b solvd in a diffrnt rotating rfrnc, instad of a transint moving msh. Th inhrnt advantag of th MRF approach was th ability to build th computational msh of ach of th rotating componnts indpndntly. A scond-ordr upwind diffrncing schm was utilizd and th standard k-ε modl was also usd for th turbulnc. Stady stat simulations wr prformd for a rang of spd ratios from 0.0 to 0.9 whil maintaining an impllr spd of 2000 r/min. Figur 2 Approach to dcras axial lngth of torus Figur 3 Computational msh

4 Pag 4 of 9 Torqu ratio Tr Impllr torqu factor λi / (10-6 min 2 r -2 m -1 ) Exprimntal Calculatd (=1) λ I Tr Spd ratio i Figur 4 Ovrall prformanc of typ 1 torqu convrtr Efficincy η / % Spd ratio i Figur Efficincy of four diffrnt typs 3.2 Rsults and Discussion Four torqu convrtrs with diffrnt flatnss ratio wr calculatd using a CFD cod in ordr to valuat th chang in thir ovrall prformanc, including fficincy η, torqu ratio Tr and impllr torqu factor λ I. Th accuracy of th valuation rsults was highly dpndnt on th accuracy of th CFD rsults. Thrfor, it was important to obtain rliabl CFD rsults. Figur 4 compars th masurd and calculatd ovrall prformanc for th typ 1 torqu convrtr. As indicatd hr, th tndncis of th xprimntal data corrlatd rlativly wll with th calculatd rsults, confirming that th computational mthod is valid in gnral. Figur shows th ovrall fficincis calculatd for all four typs of torqu convrtrs. As th flatnss ratio dcrass, th ovrall fficincy dcrass, which is quit rmarkabl at high spd ratio. Th main caus of this dclin in ovrall fficincy was attributd to a gratr loss within th fluid flow channls du to flattning. Figur 6 dscribs th torqu ratio Tr vrsus th spd ratio i with four typs of torqu convrtrs. It is of not that th typ 2 ( = 0.9 ) has narly th sam valus with th η Efficincy η / % Spd ratio i Figur 6 Torqu ratio of four diffrnt typs Torqu ratio Tr Impllr torqu factor λi / (10-6 min 2 r -2 m -1 ) Spd ratio i Figur 7 Impllr torqu factor of four diffrnt typs rfrnc typ ( = 1.0 ), and th othr typs show th lowr torqu ratio throughout th whol rang of spd ratios. Figur 7 illustrats th impllr torqu factor comparison among th four typs. Among th four typs, th typ 4 ( = 0.7 ) shows th lowst valu of impllr torqu factor λ I. Whn th flatnss ratio dcrass, th magnitud of th impllr torqu factor λ I tnds to dcras spcially at low spd ratio. Basd on th rsults in Figurs, 6, 7, it is concludd that th ovrall prformanc tnds to dtriorat as th flatnss ratio dcrass. 4 Optimal Dsign of a Flat Torqu Convrtr Th trnd in futur automatic-transmission dsigns is to achiv comparabl prformanc to traditional dsigns but with rducd mass and in lss spac. Th challng in torqu convrtr dsign is to dvlop a rducd-width torus without sacrificing prformanc. In this papr, CFD is usd to analyz numrous itrations of torqu convrtrs to optimiz th torus for th allowd spac. Th typ 4 torqu convrtr with flatnss ratio 0.18 ( = 0.7 ) was chosn as th study objct.

5 Pag of Snsitivity Analysis of Inlt and Outlt Angls Sinc th blad transmits all of th torqu of a torqu convrtr, its dsign is of utmost importanc. In fact, ach of th blads would rciv working fluid without shock, dflct th flow smoothly throughout th lngth of blad passag, and discharg th fluid at th optimum angl at all conditions of spd ratio and torqu distribution. Unfortunatly, it is vry difficult to mt optimal rquirmnts. In th prsnt study, a snsitivity analysis was usd to invstigat th ffct of th blad gomtric paramtrs on th torqu convrtr prformanc charactristics. Th main paramtrs invstigatd in this papr wr inlt and outlt angls of th impllr, turbin, and stator. To improv th dsign fficincy, a softwar was dvlopd for gnrating th blads with various inlt and outlt angls [22]. Th blads of typ 1 torqu convrtr with inlt and outlt angls shown in Tabl 2 wr chosn as th rfrnc blads in ordr to compar th prformancs of th othrs. Finally, blads of th impllr, turbin, and stator with various inlt and outlt angls (, 10, or 1 blow and abov th rfrnc valu of th paramtr) wr gnratd. Torqu convrtrs with diffrnt blads wr calculatd using th abov-mntiond computational mthod in ordr to valuat th ffct of inlt and outlt angls on thir ovrall prformanc, including pak fficincy η and stall torqu ratio Tr 0. Figur 8 shows th snsitivity of impllr inlt and outlt angls on th prformanc charactristics of th convrtr. Th impllr inlt angl β I1 rangs from 11 to 14 whil th outlt angl β I2 rangs from 3 to 6. In th rang of β I1, prformanc Tr 0 dcrass with incras of angl, whras η incrass. Convrsly, th incras of β I2 causs incras of Tr 0 and dcras of η. Figur 9 provids th snsitivity of turbin inlt and outlt angls on th prformanc charactristics of th convrtr. Th turbin inlt angl β T1 rangs from 20 to whil th outlt angl β T2 rangs from 120 to Stall torqu ratio Tr0 Pak fficincy η*/ % Impllr inlt angl β I1 / ( ) Impllr outlt angl β I2 / ( ) Figur 8 Impllr inlt and outlt angls snsitivity analysis 1. It is of not that th torqu convrtr with rfrnc blads shows th highst valu of Tr 0 among simulation cass with diffrnt β T1 and highst valu of η among simulation cass with diffrnt β T2. Th simulation cas with β T1 fiv dgr lowr than th rfrnc blad shows drastically dcrass in η. It is sn that Tr 0 dcrass with incras of β T2. Figur 10 illustrats th snsitivity of stator inlt and outlt angls on th prformanc charactristics of th convrtr. Th stator inlt angl β S1 rangs from to 11 whil th outlt angl β S2 rangs from to 40. Similarly, th simulation cas with rfrnc blads shows th highst Tr 0 valu among cass with diffrnt β S1. Prformanc η incrass first and thn dcrass with incras of β S1. It is found that both prformanc Tr 0 and η dcras with incras of β S2. Basd on th rsults in Figurs 8, 9, 10, it is concludd that th inlt and outlt angls of th impllr, turbin and stator play an important rol in dtrmining th prformanc charactristics of a torqu convrtr including stall torqu ratio and pak fficincy. Th snsitivity analysis provids usful information of th influnc of dsign paramtrs individually on th flat torqu convrtr, but not provids information on thir combinations ffct. Latr, a DOE tchniqu would b usd to gaug th combination ffct of ths six dominant paramtrs. 4.2 DOE Mthod Dsign of xprimnts (DOE) is a collction of mathmatical and statistical tchniqus to rduc th numbr of xprimnts in ordr to find th ffct of paramtrs affcting a rspons in a procss, thrby aiming for a rduction in both costs and tim [23 2]. It is also usful to obtain a grat dal of information through an action to rduc th numbr of simulations. Th aim is to slct som points that th numrical simulations should b invstigatd and can b adoptd for planning, conducting, analyzing, and intrprting controlld tsts in ordr to valuat th factors that control th valu of a paramtr or group of paramtrs. A DOE mthod sts out configurations (or arrangmnts) to b conductd using an appropriat orthogonal array; th trminology usd in ths arrays includs factors an itm that is to b varid during th simulations, lvl th numbr of tims a factor is to b varid during th simulations and configuration numbr th numbr of simulations that ar rquird to b run to complt th analysis [26]. For this papr six main gomtrical paramtrs of a torqu convrtr ar slctd as dsign variabls (factors), which ar th inlt and outlt angls mntiond abov. For ach dsign paramtr, fiv diffrnt valus (lvls) wr assignd. So 2 (L 2 [ 6 ]) configurations with diffrnt combinations wr gnratd for DOE. Th original valus of th six paramtrs ar listd in Tabl 2 and th

6 Pag 6 of 9 Stall torqu ratio Tr0 Pak fficincy η*/ % Turbin inlt angl β T1 / ( ) Turbin outlt angl β T2 / ( ) Figur 9 Turbin inlt and outlt angls snsitivity analysis Stall torqu ratio Tr0 Pak fficincy η*/ % Stator inlt angl β S1 / ( ) Stator outlt angl β S2 / ( ) Figur 10 Stator inlt and outlt angls snsitivity analysis stp valus wr chosn to b 3 for ach factor. Th final configurations for DOE can b constructd as shown in Tabl Numrical Simulation Th 2 cass with diffrnt blad dimnsions wr simulatd using th abov-mntiond mthod. Stall torqu ratio and pak fficincy wr slctd as th dynamic charactristic and conomic charactristic, rspctivly, to valuat th prformanc charactristics of th flat torqu convrtr. Th simulation rsults ar also prsntd in Tabl 3. It can b sn that among th cass, numbrs 14 and 19 hav th two bst rsults of stall torqu ratio, and numbr 19 and 1 hav th two bst rsults of pak fficincy. It is clar that th maximum stall torqu ratio and th maximum pak fficincy can not b obtaind at th sam tim. So, an optimization study is ndd to improv th ovrall prformanc of th flat torqu convrtr. 4.4 DOE Post procssing and Optimization Th procssing of th data obtaind from DOE could b dscribd as blow. Firstly, th 2 cass wr groupd by th lvls of a factor. Taking factor turbin inlt angl β T1 as xampl, fiv groups could b obtaind and ach of thm had th sam valu (as shown in Tabl 3). Th avrag valu of th stall torqu ratio Tr 0 of ach group could b calculatd as follows: K 1 = = 1.634, (1) K 2 = = , (2) K 3 = = 132, (3) K 4 = = 1.9, (4) K = = , () To b mor clar, th influnc lvls K 1, K 2, K 3, K 4, and K wr th avrag stall torqu ratio whn turbin inlt angl β T1 quald 28, 31, 34, 37, and 40, rspctivly. Thn, th pak fficincy could b procssd by th sam mthod. In addition, rang R was dfind as th diffrnc btwn maximum and minimum valus. Finally, th ovrall DOE analysis data was calculatd and shown in Tabl 4. Th rang R rflcts th influnc lvl of ach gomtrical paramtr on th hydrodynamic charactristics of a torqu convrtr. Th contribution valu C was dfind as th prcntag of th R valu of a spcific factor to th total R valus of all th factors. A factor with largr R would hav mor influnc on torqu convrtr prformanc indicators, and was considrd as an important factor during convrtr dsign. Whil factors with small rang valu R would b considrd as lss important factors during dsign procdur. It could b found in Tabl 4 that, paramtrs turbin outlt angl β T2 and stator outlt angl β S2 ar th two most important factors. To b mor prcis, th dscnding sort of rang R is β T2 >β S2 >β T1 >β S1 >β I2 >β I1 for stall torqu ratio, and β T2 >β S2 >β T1 >β I2 >β I1 >β S1 for pak fficincy. Thrfor, mor focuss ar ndd on th

7 Pag 7 of 9 Tabl 3 Configurations and simulation rsults in DOE Cas numbr Factors Rsponss Turbin inlt angl β T1 ( ) Turbin outlt angl β T2 ( ) Impllr inlt angl β I1 ( ) Impllr outlt angl β I2 ( ) Stator inlt angl β S1 ( ) Stator outlt angl β S2 ( ) Stall torqu ratio Tr 0 Pak fficincy η (%) Tabl 4 Ovrall DOE analysis data Indicator Influnc lvl Turbin inlt angl β T1 Turbin outlt angl β T2 Impllr inlt angl β I1 Impllr outlt angl β I2 Stator inlt angl β S1 Stator outlt angl β S2 Stall torqu ratio Tr 0 K K K K K R C 17% 2% 7% 13% 16% 22% Pak fficincy η (%) K K K K K R C 19% 21% 12% 16% 12% 20%

8 Pag 8 of 9 optimization of turbin outlt angl and stator outlt angl in th dsign phas, in ordr to achiv bttr prformanc of th flat torqu convrtr. It should b notd that th rsults may hav som diffrnc with th conclusions studid bfor. This is possibl causd by th lvl slction of dsign paramtrs. In th prsnt study, th dsirability function was usd to carry out th optimization [27]. Th optimization rsults dpnd on th rspons wights of stall torqu ratio and pak fficincy. In this study, optimization analysis was prformd providd that th stall torqu ratio and pak fficincy had th sam rspons wight. Th rsults show that cas 19, that is, 37 for β T1, 147 for β T2, 128 for β I1, 6 for β I2, 97. for β S1, and 1 for β S2, hav th bst ovrall prformanc of th flat torqu convrtr. Compard to th convntional product ( = 1.0 ), th flat torqu convrtr with flatnss ratio 0.18 ( = 0.7 ) is dvlopd that rduc th width of th torus by about 20%. Th axial lngth of th optimal flat torqu convrtr and its wight hav bn substantially rducd whil th valus of stall torqu ratio and pak fficincy ar only dcrasd by 0.4% and 1.7%, rspctivly. Conclusions 1. DOE mthod basd on CFD tchniqu is applid to obtain an optimizd dsign of a flat torqu convrtr gomtry. To this nd, 2 cass with diffrnt inlt and outlt angls of impllr, turbin, and stator ar dsignd, constructd and simulatd. Th main advantag of DOE is its ability to considr th combination ffct of dsign paramtrs on prformanc, as it is not limitd to traditional on-factor-at-a-tim approach. 2. Th analysis of th DOE array idntifid th dominant gomtrical influncs on th prformanc of th flat torqu convrtr. In gnral, th turbin outlt angl and stator outlt angl ar th two strongst influncs on th convrtr prformanc charactristics, including stall torqu ratio and pak fficincy. 3. Basd on th calculation rsults in DOE, dsirability function approach is mployd to optimiz th flat torqu convrtr gomtry. It should b notd that th maximum valus of stall torqu ratio and pak fficincy can not b obtaind at th sam tim. Finally, th bst dsign configuration is achivd at cas 19, that is, 37 for turbin inlt angl, 147 for turbin outlt angl, 128 for impllr inlt angl, 6 for impllr outlt angl, 97. for stator inlt angl, and 1 for stator outlt angl. Th optimization mthod first usd in prformanc improvmnt of flat torqu convrtrs can provid fundamntal guidlins for dsignrs. Authors Contributions G-QW and JC wr in charg of th whol trial; JC wrot th manuscript; JC and W-JZ assistd with sampling and laboratory analyss. All authors rad and approvd th final manuscript. Author dtails 1 School of Automotiv Studis, Tongji Univrsity, Shanghai 2014, China. 2 Institut of Industrial Scinc, Th Univrsity of Tokyo, Tokyo 13 80, Japan. Authors Information Guang-Qiang Wu, born in 196, is currntly a profssor and a PhD candidat suprvisor at School of Automotiv Studis, Tongji Univrsity, China and Institut of Industrial Scinc, th Univrsity of Tokyo, Japan. H rcivd his PhD dgr from Jilin Univrsity, China, in His main rsarch intrsts includ advancd dsign thory and mthod of th automobil. Ji Chn, born in 1988, is currntly a PhD candidat at School of Automotiv Studis, Tongji Univrsity, China. His main rsarch intrsts includ flow simulation, modification and optimal dsign thory for th torqu convrtr. Wn-Ji Zhu, born in 1989, is currntly a mastr candidat at School of Automotiv Studis, Tongji Univrsity, China. His rsarch intrsts includ flow simulation, modification and optimum dsign thory for th torqu convrtr. Compting Intrsts Th authors dclar that thy hav no compting intrsts. Funding Supportd by National Natural Scinc Foundation of China (Grant No ). Publishr s Not Springr Natur rmains nutral with rgard to jurisdictional claims in publishd maps and institutional affiliations. Rcivd: 21 July 2016 Accptd: 2 August 2018 Rfrncs [1] B Zhao, Y Wang, H Chn, t al. Hydraulic optimization of a doubl-channl pump s impllr basd on multi-objctiv gntic algorithm. Chins Journal of Mchanical Enginring, 201, 28(3): [2] D Li, R Gong, H Wang, t al. Entropy production analysis for hump charactristics of a pump turbin modl. Chins Journal of Mchanical Enginring, 2014: [3] M H Shojafard, M Tahani, M B Ehghaghi, t al. Numrical study of th ffcts of som gomtric charactristics of a cntrifugal pump impllr that pumps a viscous fluid. Computrs & Fluids, 2012, 60: [4] L Tan, B Zhu, S Cao, t al. Influnc of blad wrap angl on cntrifugal pump prformanc by numrical and xprimntal study. Chins Journal of Mchanical Enginring, 2014, 27(1): [] G Q Wu, P Yan. Systm for torqu convrtr dsign and analysis basd on CAD/CFD intgratd platform. 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