Effects of Surface Roughness and Fluid on Amplifier of Jet Pipe Servo Valve

Transcription

1 The Intenational Jonal Of Engineeing And Science (IJES) Volme 5 Isse Pages PP -3 6 ISS (e): ISS (p): Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve Xan Hong Son PHAM Depatment of Mechanical Engineeing, HoChiMinh Cit Univesit of Technolog, Vietnam ABSTRACT In manfacting pocess of jet pipe electo-hdalic sevo valve, it mst be having a lot of eos in the inne wall of sevo valve components, which flid flows will have a cetain oghness. Jet pipe electo-hdalic sevo valve, in fact, can se vaiet of flid ding its woking. With CFX softwae, this aticle stdies effect of sface oghness of pats and woking flid on pesse chaacteistics of amplifie of pilot stage in jet pipe sevo valve. Thogh mathematical models and simlation, it is shown that effect of wall oghness of pats on flow chaacteistics of the pilot stage amplifie is mch. Analsis of man diffeent oghness, it is fond ot that the geate sface oghness is, the smalle velocit of jet flow is, and the ecove pesse deceases bt the magnitde of change is not mch. In addition, the elationship between the viscosit of flid and the pesse chaacteistics of the pilot stage is close. Ke wods: Rogh sface; Smooth sface; Flid; Amplifie Date of Sbmission: 7 Ma 6 Date of Accepted: 9 Octobe I. ITRODUCTIO Jet pipe electo-hdalic sevo valve has high eliabilit and abilit in polltion esistance, which can develop in the lage civil aicaft. Compaing jet pipe sevo valve with nozzle flappe sevo valve, it can been seen that pesse and volmetic efficienc of jet pipe sevo valve each to 7 pecent while the nozzle flappe sevo valve is abot 5 pecent, as a eslt, the jet pipe sevo valve can podce bigge pesse and contol flow, so moe and moe athos std jet pipe electo-hdalic sevo valve. Using CFD simlation softwae, jet pipe sevo valve is stdied nde diffeent woking media, stcte size effects on flow field chaacteistics b Li, et al., []. Mala,et al, [] se model of sface oghness and viscosit (RVM) to simlate inflence of wall oghness on lamina flow in mico-channel. omall, the existence of oghness will incease tansfe of momentm fom bonda lae nea wall, the additional momentm tansfe can be led into the model of edd viscosit tblence which is simila to the viscosit of oghness µr. If the vale of µr nea wall is bigge, the channel cente gadall disappeas. The eslts of nmeical simlation of RVM model and thei expeiment eslts ae ve well. Tansition in advance cased b sface oghness can be well explained b RVM model (Mala, et al) [3]. ie simlated pots of valve spool of cicla seam, flappe nozzle valve with wate and othe hdalic components in the fom of a tpical oifice nde high pesse chaacteistics [4]. YeHa Yang, etc associated methods of mathematical modeling, simlation and expeimental eseach fo flow field of jet pipe electo-hdalic sevo valve pe-stage, ca ot theoetical analsis and expeimental eseach, the integated se of comptational flid dnamics, theo of cavitation of mltiphase flow, and inflence of vaios paametes on flow field wee analzed [5]. Inflence of smmetic distibtion between two paallel plates of thee-dimension oghness on pesse-diven flow and velocit field thogh mico-channels,.< Re <, is eseached b H, et al. [6], the conclsion is the existence of oghness will incease pesse dop abot. pecent, simltaneosl, geometic shape, size, gap and plate spacing ae involved. Thogh the modified model of viscosit coefficient of sface oghness fo gas flow within mico-tbe, Chen, et al., [7] eseached the inflence of wall sface oghness of mico-tbe on gas flow within mico-tbes. The nmeical simlation ageed well with the expeimental data. Using the Flent and Gambit softwae, Ji, et al., [8] analzed effect of jet pipe amplifie stcte on its static chaacteistics, and pesented flow chaacteistics nde diffeent deflections of jet pipe. Stokes flow nea wall of sphee nde the condition of ogh sface was stdied b Lecoq, et al., [9], the tansfomed ogh sface into an effective smooth sface, simltaneosl, in nmeical analsis, slip wall condition was sed instead of no slip wall condition to std sffeable esistance of sphee. Yang, et al., [] analzed theoetical and expeimental eseach on flow field chaacteistics of oifice of cicla tbe, cone valve, and cavitation chaacteistics at valve pots also lanched a discssion on the eseach eslts achieved in this pape. Using matching expansion method, Michael, et al., [], obtained slip coefficient of flowing thogh ogh sface. Zho, et al., [] established jet contol eqations fo abasive two-phase of liqid-solid, sing the standad k-e tblence model The IJES Page

2 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve in Flent softwae to ca ot the nmeical simlation, and the effect of sface oghness on steam-flow is conclded. Jansons poposed mico-scale slip bonda condition nde ogh sface [3]. Yao, et al., stdied the easonabilit and applicabilit of the flow condctance theo fo jet pipe valve accoding to jet flow dnamics, the inside adis of jet pipe was eplaced b a flow adis in the theo of flow condctance [4]. Tck and Kozobov [5] eseached a modified slip bonda condition to epesent the effects of small oghness-like petbations to an othewise-plane fixed wall which acted as a bonda to stead lamina flow of a viscos flid. This bonda condition involves a constant appaent backflow at the mean sface. ie, et al., [6] stdied the pesse distibtion between two thottles of two-step thottle, and theoetical analsis o expeimental eseach fo flow field chaacteistics of thottle was caied ot. Thogh the above close analses, eseach on the inflence of sface oghness and flid on hdalic amplifie of jet pipe is also ae, so this pape is poposed. II. SIMULATIO OF THE MIDDLE OF FLOW FIELD FOR JET PIPE AMPLIFIER. Schematic diagam and woking pinciple of jet pipe electo-hdalic sevo valve A two-stage, fo-wa, closed pots electo-hdalic flow contol sevo valve is assmed to be the powe contol device fo the hdalic sstem which was analzed. It convets electic signal into a hdalic signal, with fast dnamic esponse, high pecision, small hsteesis, good linea degee, the eqiements of contol signal ae small. It is also a kind of high pefomance and high pecision contol component. The basic elements of a jet pipe electo-hdalic sevo valve ae shown in Fig., in which thee ae two magnetic poles of toqe moto. A jet pipe electo-hdalic sevo valve can be sepaated into two-stages: The pilot-stage incldes the toqe moto, jet pipe, flexe tbe and eceive holes. The second stage bod incldes the spool and sleeve assembl. The movement of the spool opens oifices ae connected to a pesse sppl and sink and to both sides of the main actato piston. -Uppe pemanent magnet; -Contol coil; 3-Jet pipe; 4-Receive holes; 5-Valve spool; 6-Valve bod; 7-Valve sleeve; 8-Feedback sping; 9-Lowe pemanent magnet; -Flexe tbe; -Amate of jet pipe Fig. Schematic diagam of jet pipe sevo valve Hdalic flid at sstem pesse tavels thogh the pilot-stage wie mesh filte into a feed-tbe and ot of the pojecto jet. The pojecto jet diects this hdalic flid steam to two eceives, each of which is connected to the second stage spool s end chambes. The pilot-stage toqe moto eceives an electical signal (cent to the coils) and convets it into a mechanical toqe on the amate and jet pipe assembl. The toqe otpt is diectl popotional to the inpt cent. As moe cent is applied to the valve, the geate foces ae exeted to otate the amate assembl aond its pivot point, eslting in moe flid impinging on one eceive than the othe. The eslt of diffeential pesse between the spool s end chambe tigges spool movement and, in tn, ncoves stage poting casing flid to flow to and fom, depending on spool diection, the two valve contol pots. The diection of spool displacement is opposite to the jet pipe otation. As the spool moves, the feedback sping geneates a foce at the jet pipe which opposes the toqe moto s foce. The spool contines to move ntil the foce geneated b the feedback sping eqals the foce podced b the toqe moto. Then the jet pipe position is etned to be cented ove the two eceives. A small diffeential pesse sall emains acoss the ends of the spool to ovecome Benolli flow foces that tend to close the valve and feedback sping foce. The spool displacement is popotional to the contol cent in the toqe moto. As the spool moves, flid is meteed popotionall to and fom the second stage contol pots. When the inpt signals to the toqe moto va in amplitde and polait, the second stage spool accatel follows the signals and metes flid accodingl [7~9]. The IJES Page

3 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve. Simlation of the middle of flow field fo jet pipe amplifie Eqation of avie-stokes is the pinciple of consevation of momentm in the fom of flid movement, the momentm eqation of the diection i is given as follows t i j F i i j i x j P x i x j x j x i () whee, P is pesse; F i is extenal foce; ν is dnamic viscosit; ρ is densit. Fo lamina flow and all the elevant length, the can inclde tblence in the lattice, diectl solve the -S eqation is possible (b diect nmeical simlation). In geneal, ange of sitable citeion poblems is even geate than ange of possible model of toda s massive paallel compte. In these cases, the tblence simlation needs to intodce tblence model. Lage maelstom simlation, and RAS expession (avie- Stokes eqation of Renolds aveage), o model of k-ε model and Renolds stess togethe, dealing with two kinds of technolog of these citeia. In man instances, -S eqation o othe eqations ae solved simltaneosl. k-ε model is fo impoving the mixing length model and algebaic expession of tblence length dimension of wall complex flow. Eqation of k is conveance of tblent kinetic eneg, and eqation of ε is tblent kinetic eneg dissipation ate. Standad model of k-ε is intodced b vaiable tblent kinetic eneg and contol eqation of tblent kinetic eneg dissipation ate. The continit eqation o momentm eqation becomes t k i T whee T t T p T i is phsical vecto, T is empiical constant, () µ is calclation viscosit of effective tblence, µ i is tblent viscosit, p is amending pesse. The se of the simplified thee-dimensional models is shown in Fig.. Accoding to the smmet model, it can be ct fom the smmet plane. In pepocessing of CFX, flid and flow condition ae set as follows: Flid to be sed is aviation hdalic oil of, densit of 85 [kg/m 3 ], dnamic viscosit of.5 [kg/ms], activated tblence model, and sing the standad model of k-ε. Assming that thee is no heat exchange, and heat tansfe eqations closed-fom, the inlet pesse is p s = [MPa], the otlet pesse of [MPa], the atmospheic pesse of atm, the gap between nozzle and eceive holes is.6[mm], the jet pipe diamete of =.3[mm], the eceive holes diamete of R=.3[mm], and the coss-section is smmetical, the maximm nmbe of iteations of solving is times, the maximm esidal eo is., othe sfaces ae no-slip walls. Fig. Simplified 3D model fo jet pipe of pe-stage in the middle and CFX mesh geneation III. EFFECT OF SURFACE ROUGHESS O PRESSURE CHARACTERISTICS Ding flowing fom the inlet to the otlet, flid will inevitabl have pesse loss, which incldes local pesse loss cased b change of pipeline section o eneg loss cased b votex flow neab jet pipe exit, and local pesse loss cased b flowing of flid in eceive holes. Fthe, ding flowing in pipeline of wall oghness, flid will have pesse loss and eneg loss cased b its viscosit. The IJES Page 3

4 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve 3.Mathematical desciption of flow nea wall egion Fo fll developed tblent flow on fixed wall, in diffeent distances along wall nomal, flow can be divided into the wall aea and the coe egion. It can be consideed fll developed tblence in the coe egion. The wall aea is affected obviosl b wall sface, and can be divided into thee laes: viscos sb-lae, tansition lae, logaithmic lae. Viscos sb-lae is a ve thin lae that clings to solid wall, the viscos foce plas leading ole in exchange of kinetic eneg, heat and mass, and all flow is lamina, velocit component paallel to wall sface along diection nomal is linea distibtion. Tansition lae is otside of viscos sb-lae, in which effect of viscos foce and tblent shea stess is abot eqal, the flow condition is moe complex. Becase of the tin thickness of tansition lae, it sall doesn t daw obviosl in poject, and mege into logaithmic lae. Logaithmic lae is in the otemost lae, then the impact of viscos foce is not obviosl, the tblent shea stess is mainl dominant, flow is in fll developed tblence stats, velocit distibtion is nea the logaithmic lae. To descibe viscos lae, two dimensionless paametes ae intodced, and fomlae of velocit and distance ae given as follows and w (3) whee, τ is the shea velocit,. 5 w is time-aveage velocit, τ w is the wall shea stess, is the distance fom the wall. Fo the flow nea the wall, and at low Re nmbe, tblence is not fll developed, effect of the tblence implse is not as big as flid viscosit. omall, sing of the wall fnction method and the model of k-ε in low Re nmbe, and coodinate the standad model of k-ε can sccessfll solve poblems of flow calclating fo the nea wall and low Re nmbe. The wall fnction fo the phsical qantit on the wall is diectl linked to the nknown volme of tblence coe aea. It mst be sed coopeativel with model of k-ε in high Re nmbe. The basic idea of the wall fnction is soltion model of k-ε b sing flow of tblent coe aea, and it isn t solved in the wall sface. Use diectl semi-empiical fomla, not onl avoid linking between phsical qantit and solving vaiable qantities bt also avoid sing calclation of viscosit tblence model. Thogh low Re nmbe method on the wall nomal diection b sing the efined mesh (ve thin expanded lae) it can solve desciption of bonda lae..3 k k 4 C k R C (4) whee, C µ is constant of expeience, tblent viscosit is the same tblent kinetic eneg k, C is constant elated to sface oghness, κ is the Kaman constant, R is eqivalent sand oghness. Using ASYS CFX method fo a gadal change to the wall fnction and low Re nmbe method, and withot loss of pecision. Viscos sb-lae consides + = +, and in the log-law egion, the nea wall tangential velocit is elated to the wall shea stess. 3. Analsis of fiction coefficient fo diffeent flid flows It mst be some eos in the manfacting pocess of jet pipe sevo valve, the inne wall of jet pipe modle is sface that flid ns thogh, and it also has cetain oghness. In addition, the flowing pocess of flid fom the inlet to the otlet is tblence. These factos will inevitabl podce pesse loss along the wa. Two flctating velocit components podced in tblent flow ae the diffeence between lamina and tblence, inclding ' fo the velocit in the flow diection and v' fo the velocit in the pependicla to the flow diection. Viscos sb-lae is a ve thin lae close to solid wall, the viscos foce plas leading ole in exchange of kinetic eneg, heat and mass, and almost all flow is lamina. The velocit component paallel to the wall in the nomal diection along the sface is linea distibtion.consideing the Re nmbe, flowing in thin tbe is tblence if Re > 3, ths thee is a elation between pesse loss along the length of the tbe Δp and othe paametes sch as velocit, densit, diamete, length and fiction coefficient, and given as following: The IJES Page 4

5 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve V p D (5) whee V is the mean flid velocit, χ is the length of tbe, λ is the fiction damping, D is the diamete of tbe, ρ is the flid densit. Fom (5), it can be seen that the along wa pesse loss in thin tbe Δp is popotional to the fiction damping λ. The geate the oghness is, the bigge the pesse loss is. Theefoe, in jet pipe electo-hdalic sevo valve, the oghness of thin tbe sface of hdalic amplifie mst be fitting. Convesel, if thee is no oghness in the inne sface of jet pipe, the flow in thin tbe is stck. Coefficient of fictional esistance is a dimensionless facto, which mainl depends on the tbe diamete o velocit, viscosit and densit of flid, and it is also a fnction of the wall oghness. In thin tbe of sface oghness, assming that e is the absolte oghness and δ is the thickness of lamina bonda lae. Becase coefficient of fictional esistance is a fnction of the inne wall oghness, so it depends on the size and the shape of oghness facto. Fom the specific oghness facto e, setting p the atio of e/d and it is called elative oghness. Thogh elationship between e and δ, flid motion is divided b thee cases, inclding hdalicall smooth flow (e < δ), hdalicall ogh flow (e > δ) and tblent tansition (e = δ). Hdalicall smooth is stead tblence: when the lamina bonda lae thickness is geate than the absolte oghness (e < δ), the eneg loss depends on flid viscosit. Wall oghness almost isn t affected b changing of flow velocit in lamina bonda lae egion, and flid flow itself geneates tblence at this moment, i.e. λ = f(re). Hdalicall ogh is ogh wall tblence: when the absolte oghness is geate than the thickness of lamina bonda lae (e > δ), the oghness mainl cases tblence to flid flow, hence, flowing will enconte obstacle of oghness, then geneate esistance. The elative oghness e/d is fomed fom diffeent sface oghness elements, ths it inflences to flow chaacteistics of hdalic amplifie stongl, i.e. λ = f(e/d). If coefficient of fictional esistance inceases, eneg loss also inceases, theefoe, ecove pesse will be small. Tblent tansition: when the absolte oghness and the thickness of lamina bonda lae ae the same (e = δ), thee ae two easons of ielding tblence, inclding tblent motion chaacteistics de to oghness and smooth motion chaacteistics, the exet togethe thei inflence, i.e. λ = f(e/d, Re). Pesse loss is the intenal oghness of tbe wall and eneg loss is flid viscosit will togethe occ, ths ecove pesse will be small, too. The oghness of the inside tbe wall of jet pipe pe-amplifie is shown in Fig.4 If flid in tbe is lamina flow, coefficient of fictional esistance is: 64 Re.Accoding to Pandtl s law, total esistance in tblence eqals to the sm of viscos esistance and additional esistance d d (6) d d whee χ is Pandtl s mixing length, χ = κ. ; µ is dnamic viscosit; ν is kinetic viscosit. When > δ, total esistance in tblence is d d So d. τ d d d C (7) Fig.4 Local wall oghness of jet pipe pe-amplifie The IJES Page 5

6 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve The IJES Page 6 Fig.5 Diffeential of ing aea () Fiction esistance coefficient analsis of hdalic smooth (semi-empiical fomla) If the lamina bonda lae thickness is geate than the absolte oghness e 5, it is called hdalic smooth. Consideing flow ate of the lamina bonda lae w and the bonda lae thickness. Let: w, then it can obtain: (8) In addition, fom (7) it can be seen that: C w, then C C C (9) Combining Eq. (9) to Eq. (7), it can be obtained as follows: G () whee G,, and Accoding to conditions of the ikadse s hdalic smooth expeiment, it is κ of.4 and G of 5.5. On the wet aea of cicle, consideing the distance fom the cicle cente to the diffeential of the ing aea is ( - ), and detemination of the ing aea is shown in Fig.5. Let d d Q d d d A A Q Q d d 4 A A Q whee dω is the ing aea, Q is the volme flow ate thogh thin tbe. Meanwhile, d and 4 d Moeove, lim, and lim. This indicates that: V 3 () Then, 8 V

7 Fictional esistance coefficient Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve V 8 Combining to Eq. (), it is ewitten as follows: V 8.88 Re. 9.6 log 8 3 Re 8 8 Re. 9 o whee V is the mean velocit on the coss-section. Range of Re nmbe is: 3 3 < Re < 6. () Fiction esistance coefficient analsis of hdalic ogh (semi-empiical fomla) If the lamina bonda lae thickness is smalle than the absolte oghness () ogh. Then the expession of velocit given as follows: w me const Ths, const w ( m ) ( e ) (3) whee w is wall velocit of lamina bonda lae nde the condition of = me. Combining Eq. (3) to Eq. (7), the velocit distibtion is ewitten as follows: ( m ) w e Let G ( m ), then w me G 3 D B 8 8 e 5, it is called hdalic Accoding to conditions of the ikadse s hdalic ogh expeiment, it is κ of.4 and G of Ths, D (4).6.3 log e Fom Eq.(4), it can be seen that esistance coefficient λ is popotional to the absolte oghness e. If esistance coefficient λ and e incease togethe, level of tblence will incease, then eneg dissipation will also incease and stongl affect to the pesse magnitde in jet pipe. Associating Eq. (5) and Eq. (4), it can be seen that when vale of oghness is bigge, eneg loss of flid in tbe is also bigge, as a eslt of this, the pesse loss along the length of the tbe Δp is popotional to the absolte oghness e. Calclation of fiction coefficient shold give in Fig. 6a and Fig. 6b. e Renolds nmbe. Coefficient of calclating fiction esistance. ikadse s fictional esistance coefficient Fig.6a Coefficient of λ fo hdalic smooth egion. The IJES Page 7

8 Fictional esistance coefficient Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve Relative oghness,d/e. Coefficient of calclating fiction esistance. ikadse s fictional esistance coefficient Fig.6b Coefficient of λ fo hdalic ogh egion 3.3 CFD simlation in cases of wall oghness Aviation hdalic flid is sed, its densit is 85 [kg/m 3 ], kinetic viscosit of.5[kg/ms]. Tblent model and standad model of k - ε ae activated. Assming thee is no heat exchange, heat tansfe is closed, the atmospheic pesse is [atm]. Taking smmetic plane of tbe while othe sface is not slippe, its wall oghness is e = 6.4 [µm]. Simlation paametes fo pesse chaacteistics ae shown in Table. Reslt of simlation CFD shold look like Fig. 7. Accoding to Fig.7, it can be seen that flow chaacteistics ae not affected mch in case of the wall oghness of 6.4[µm], and its flow is simila. ode velocities on a cosssection C which is pependicla to smmetic plane ae analsed, C is located the inne jet pipe, its distance fom the nozzle end is.45[mm]. Velocit distibtion on coss-section nde diffeent wall oghness is shown in Fig.8. Fig.7 Compaison of clod image of flow velocit fo smooth wall with ogh wall Table. Simlation paametes fo pesse chaacteistics Paamete Vale Bonda condition of the inlet p s [MPa] Bonda condition of the otlet [MPa] Wall oghness e 6.4 [µm] Densit of aviation oil 85 [kg/m 3 ] The nmbe of gid nodes on coss-section C in nozzle is ten, i.e. velocit distibtion on coss-section has ten data points while the wall sface doesn t inclde. Becase of no slip wall, flid velocit in wall is zeo. In Fig.8, thee is diffeence in velocit of nodes on coss-section C. At the same locations on coss-section, velocit of point in case of ogh wall is slowe than velocit of point in case of smooth wall. Fom cve to cve, velocit is distibted with the oghness in tn as follows: e = ;.8;.6; 3. and 6.4[µm]. It can be seen that vale of oghness inceases, the jet velocit will decease, bt the change of velocit is limited. The velocit at coss-section coe in simlation CFD fo pesse chaacteistics is shown in Table. In case of smooth wall, the velocit at coss-section coe is 43[m/s] while the velocit is 4.[m/s] in oghness wall, e = 6.4[µm]. The IJES Page 8

9 Pesse dop [MPa] Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve Table. Flid velocit at coss-section coe nde diffeent sface oghness e [µm] V [m/s] Pesse dop affected b wall oghness is shown in Fig.9. Velocit distibtion on coss-section C[m/s] Distance fom jet pipe cente to diffeent adii [mm] Fig.8 Velocit distibtion nde diffeent wall oghness Fig. 9 Pesse dop affected b wall oghness Theefoe, the changes of wall oghness will impact on pesse loss Δp a in thin tbe. Fo the left eceive hole, the ecove pesse in the case of smooth wall mins the ecove pesse in the case of ogh wall eqals to the pesse loss Δp a, and that is the pesse loss of flid in the left eceive hole becase of the ogh wall. In case of C v =.9 and d =.3[mm], the appoximate fomla of the pesse dop can be given as follows p p p p s i s i p a d C v.55 log e 9.46 log e 3.73 (5) whee p p p, a a a p a is the ecove pesse in smooth wall, and is the ecove pesse in ogh wall. p a Wall oghness, e xe-6 [m] p s is the sppl pesse, p i is in-between pesse existing at the sface of eceive holes, χ is the length of thin tbe, e is the absolte oghness. IV. EFFECT OF FLUID VISCOSITY O PRESSURE CHARACTERISTICS 4. Relation between the viscosit of flid and the pesse loss Viscosit is a popet of flid to pevent occing itself shea defomation, it exists in inside flid. To ovecome its own intenal fiction is bond to wok. Ths, viscosit of flid is the oot of foming the loss of mechanical eneg. Conside a thin tbe of cicla coss-section, foce balance diagam of flow volme molecla as shown in Fig. The IJES Page 9

10 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve R d x + d P x P x + d x R v P P d x Fig. Foce balance diagam of flow volme molecla Fom Fig., foce balance eqation fo flow volme molecla is given b P d P d d x d x x x x x d x d V x R d P x 4 d x R P P d x d P d x And the aveage velocit is detemined fom its definition, it gives R R d P (6) d x x x R 8 d x P P P Q 3 V D 4 P D (7) 8 The IJES Page d d d P x d d d x x x x Fom Eq.(7), it can be seen that paametes of χ and D ae constants in jet pipe electo-hdalic sevo valve, theefoe, the pesse loss ΔP is not sbodinate to χ and D. Fthemoe, the gap between eceive holes and nozzle end, b, is a constant, ths the volme flow ate Q does not va eithe. It has been fond that the pesse loss ΔP is onl sbodinate to the dnamic viscosit, µ, and the geate the dnamic viscosit is, the moe the pesse loss has. In addition, the pesse loss is popotional to viscosit of flid, and if thee is no fiction coefficient of flid flow, the pesse loss will be zeo. Theefoe, thee is a close elation between the pesse loss and viscosit of flid, and in jet pipe electo-hdalic sevo valve, viscosit of woking flid shold be sed as small as possible. 4. CFD simlation fo pesse chaacteistics of jet pipe amplifie nde diffeent woking flid Using simplified 3D model and the mesh of Anss CFX softwae, flow field is simlated nde diffeent woking flids sch as aviation hdalic oil, jet fel 3 and hdalic oil HM 46. Jet fel 3 can satisf the oil eqiement fo flight of high altitde o cold zone and spesonic as it has themal stabilit o esistance of oxidation. This is highl clean and has no mechanical impities o moiste and no hamfl sbstances, especiall low slf. Hdalic oil HM 46 is a high pefomance anti wea hdalic oil developed fo sing in high pesse hdalic sstems opeating nde modeate to sevee conditions in mobile sevice. It has excellent oxidation esistance, good anti-foam o themal stabilit. Fthemoe, its foam can qickl disappea nde conditions of mechanical vigoos sti. Paametes of woking flids ae shown in Table 3. Table 3 Paametes of woking flids Paametes Aviation oil Jet fel 3 Oil HM 46 Densit [kg/m 3 ] Kinematic viscosit at C [mm /s] 5 56 Bonda condition and stctal paametes of valve fo simlation as follows - Diamete of jet pipe nozzle is.3[mm], diametes of eceive hole is.3[mm], the gap between nozzle end and eceive holes is.5[mm], woking liqid is hdalic oil HM 46, its densit is 87[kg/m 3 ], and its dnamic viscosit at C is.357[kg/ms]. - The inlet pesse is p s =[MPa], the otlet pesse is [MPa], the atmospheic pesse is [atm]. Using activated tblence model and the standad k ε model. - Smmetic coss-section is sveed, and the inne of jet pipe is smooth wall of non-slip sface. Flow field chaacteistics of jet pipe in the middle ae shown in Fig.a, and Fig.b. To maste effect of woking flid on the ecove pesse, it is necessa to ca ot simlation of flow field nde diffeent woking flid and diffeent positions of jet pipe, wheeb the pesse chaacteistic is obtained. Simlation eslts ae shown in Fig.a and Fig.b.

11 Load pesse PL [MPa] Recove pesse Pa [MPa] Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve Fig.a Velocit diagam of jet pipe in the middle Fig.b Pesse diagam of jet pipe in the middle Fig.a. Recove pesse in the left eceiving hole Jet pipe deflection Xj [mm] / Oil HM 46. / Aviation oil. 3/ Jet fel Jet pipe deflection Xj [mm] / Oil HM 46. / Aviation oil. 3/ Jet fel 3 Fig.b. Load pesse p L p a The IJES Page

12 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve It is fond ot fom Fig.a that flow of oil HM46 at the jet pipe end is significantl weake than flow of jet fel 3, while the ecove pesse is smalle than the ecove pesse of jet fel 3 at eceive holes. This happens becase viscosit of oil HM 46 is heav, and the effect of viscos esistance stengthens, flidit weakens, theefoe eneg loss inceases. Obviosl, the ecove pesse in eceive holes inceases nde the aise of jet pipe deflection, bt it is non-linea change. It is shown b Fig.b that the load pesse is basicall popotional to the jet pipe nozzle deflection. It can be seen that the geate viscosit is, the smalle load pesse is, bt lineait of the load pesse cve is also bette. The load pesse of jet fel 3 is the biggest, on the conta, the lineait of load pesse cve of oil HM 46 is the best bt its magnitde is the smallest, howeve, vaiation ange is limited. V. COCLUSIO Thogh mathematical models and simlation, it is shown that effect of wall oghness of the jet pipe sevo valve pats on flow chaacteistics of pilot stage amplifie is ample.thogh analsis of man diffeent oghness, it is fond ot that the geate sface oghness is, the smalle velocit of jet flow is, and the ecove pesse deceases bt the magnitde of change is not mch. In addition, the elationship between the viscosit of flid and the pesse chaacteistics of the pilot stage is close. In condition of the sppl pesse is [MPa], diametes of eceive holes and jet pipe ae.3[mm], wall oghness is 6.4[µm], aviation oil, jet fel 3 and oil HM 46 ae sed, it can be seen that the geate viscosit of flid is, the geate viscos stess in flid is. A pat of mechanical eneg of flid is lost becase of the convesion of eneg into heat, and then total of mechanical eneg in flid deceases. In pocess of change kinetic eneg into pesse eneg, the ecove pesse of the pilot stage amplifie will decease in eceive holes. REFERECES [] Li R.P., ie S.L., et al. Flow chaacteistics simlation of jet pipe sevo valve woking in diffeent medim based on CFD. Jonal of Machine Tool and Hdalics. Vol.39, o.3, (). [] Mala G.M., Li D.Q. Flow chaacteistics of wate in mico-tbes. J. Heat Flid Flow. Vol., (999), pp [3] Q W.L., Mala G.M. and Li D.Q. Pesse-diven wate flows in tapezoidal silicon mico-channels. Jonal of Heat Mass Tansfe, 43, (), pp [4] ie S.L., W Z.J., et al. Expeimental investigation on flow chaacteistics of annla gap dampe in wate hdalics. Poceeding of 6 th ICFP, Hangzho, Apil, (5), pp [5] Yang Y.H. Analsis and expeimental eseach of pe-stage jet flow field in hdalic sevo valve. Dissetation of Habin Institte of Technolog, (6). [6] H Y.D., Wene C., Li D.Q. Inflence of thee dimension oghness on pesse diven flow thogh mico-channels. Jonal of Flid Engineeing, 5, (3), pp [7] Chen B.Y., Yao Z.H. Effect of sface oghness on gas flow in mico-channels. Chinese Jonal of Applied Mechanics. Vol., o.3, (3), pp: -5. [8] Ji H., Wei L.J., et al. Investigation to the flow of jet pipe amplifie in a sevo valve. Jonal of Machine Tool and Hdalics. Vol.36, o., (8). [9] Lecoq.A., Cichocki R., et al. Dag foce on a sphee moving towads a cogated wall. Jonal of Flid Mechanics, 53, (4), pp [] Yang Y.S., Zhang T.H., et al. Design of two-step conical thottle and its pefomance test. Jonal of Hdalics and Pnematics. Vol., (), pp. -5. [] Michael J.M. and Stephen H.D. Slip ove ogh and coated -sface. Jonal of Flid Mech, 73, (994), pp [] Zho Z.G. Reseach on mechanism of affect fom sface oghness to jet pipe pefomance. Dissetation of Sothwest Univesit of Science and Technolog, (7). [3] Jansons K.M. Detemination of the macoscopic slip bonda condition fo a viscos flow ove a andoml ogh sface with a pefect slip micoscopic bonda condition. Jonal of Phsical Flid. Vol.3, o., (988), pp.5-7. [4] Yao X.X., et al. Reseach on pesse chaacteistics of jet pipe sevo valve. Jonal of Missiles and Gidance. Vol.4, (), pp [5] Tck E.O., Kozobov A. Lamina oghness bonda condition. Jonal of Flid Mech., 3, (995), pp [6] ie S.L., et al. Reseach on pesse distibtion between two thottles of two-step thottle and its load igidit chaacteistics. Jonal of Hdalics and Pnematics. Vol.8, (5), pp The IJES Page

13 Effects of Sface Roghness and Flid on Amplifie of Jet Pipe Sevo Valve [7] Yin Y.B., Meng W. Chaacteistics of electo-hdalic sevo valve with an asmmetic nozzle flappe. Chinese Jonal of Mechanical Engineeing. Vol., o.8, (), pp [8] Yin Y.B., et al. Reseach on asmmetic high-speed pnematic sevo valve. Jonal of Flid Powe Tansmission and Contol. Vol., o.3, (7), pp [9] Yin Y.B., et al. Analsis of toqe moto stiffness of electo-hdalic sevo valve. Jonal of Machine Design and Reseach. Vol.5, o.5, (9), pp The IJES Page 3