Aerodynamic Study of Two Opposing Moving Trains in a Tunnel Based on Different Nose Contours

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1 Journal of Appled Flud Mechancs, Vol. 10, No. 5, pp , 017. Avalable onlne at ISSN , EISSN DOI: /acadpub.afm Aerodynamc Study of Two Opposng Movng Trans n a Tunnel Based on Dfferent Nose Contours W. H. L, T. H. Lu, J. Zhang, Z. W. Chen, X. D. Chen and T. Z. Xe Key Laboratory of Traffc Safety on Track, Mnstry of Educaton, School of Traffc and Transportaton Engneerng, Central South Unversty, Changsha , Hunan, Chna Correspondng Author Emal:lwh@csu.edu.cn (Receved March, 017; accepted May 8, 017) ABSTRACT It s well known that the tran nose shape has sgnfcant nfluence on the aerodynamc characterstcs. Ths study explores the nfluence of four knds of nose shapes (fusform, flat-broad, bulge-broad, ellpsodal) on the aerodynamc performance of two opposng hgh-speed trans passng by each other through a tunnel at 50 km/h. The method of three dmensonal, compressble, unsteady Reynolds-averaged Naver-Stokes equatons and RNG k-ε double equaton turbulence model was carred out to smulate the whole process of two trans passng by each other nsde a tunnel. Then the pressure varatons on tunnel wall and tran surface are compared wth prevous full-scale test to valdate the numercal method adopted n ths paper. The assessment characterstcs, such as transent pressure and aerodynamc loadng, are analyzed to nvestgate the nfluence of nose shape on these assessment parameters. It s revealed that aerodynamc performance of trans whch have longtudnal nose profle lne B (fusform, flat-broad shape) s relatvely better when passng by each other n a tunnel. The results can be used as a gudelne for hgh-speed tran nose shape desgn. Keywords: Hgh-speed tran (HST); Nose shape; Ralway tunnel; Transent pressure; Aerodynamc loadng. NOMENCLATURE EX Tunnel Ext EN Tunnel Entrance k knetc energy of turbulence NN Nose and Nose NT Nose and Tal MPW Mcro Pressure Wave p mean pressure TT Tal and Tal u μ μ t μ eff ρ ɛ mean velocty dynamc vscosty of the ar turbulent vscosty sum of knetc and turbulent vscostes ar densty turbulent dsspaton rate 1. INTRODUCTION In recent years, wth the ncrease of ralway vehcle speed, a seres of aerodynamc ssues are provoked by a hgh-speed tran suddenly enters nto a tunnel, ncludng transent pressure both on tran surface and tunnel wall (Kwon et al. 003; Rccoa et al. 007), mcro pressure wave (MPW) at tunnel portal (Ozawa et al.1988), slpstream n tunnel et al. (Glbert et al. 013, Yang et al. 013). These effects would lead to passenger dscomfort, envronmental nose and potental damage to the tunnel facltes and vehcle body (Wttkowsk et al. 015). Hwang et al. (013) reported that when two opposng movng trans passng by each other n a tunnel n partcular, the pressure varaton and aerodynamc loadng actng on tran body would be much stronger and the flow phenomenon s more complcated than that of a sngle tran passng through a tunnel. Studes to solve the aerodynamc problems related to two trans meetng n a tunnel were performed lately. Chu et al. (014) carred out several numercal calculatons to explore the nfluence of the vehcle speed, the blockage rato, the tunnel length and the ntersectng locaton on the tunnel pressure waves generated by the trans. Zhang et al. (011) conducted a numercal study to solve the flow around two hgh speed trans passng by each other at the same speed n a long tunnel. Fu et al. (1995) revealed that when two opposng

2 Fg. 1. Dfferent longtudnal and horzontal nose profles of hgh-speed tran. trans encounter each other n a tunnel, the trans are frstly pushed laterally away from each other due to the hgh pressure regon on tran nose, but the sde force changes the drecton and pushes the trans towards each other when they are paralleled sde by sde. In addton, t was revealed that the lft force was nsgnfcant and can be neglected n ths ssue compared to the drag and sde force. It s acknowledged that the tunnel cross-sectonal area should be enlarged or the cross-sectonal area of the tran body should be dmnshed to lower the aerodynamc effects (Xang et al. 010, Ku et al. 010). For ths purpose, the cross-sectonal area of present hgh-speed tran gets smaller whle the tunnel becomes larger than before. However, t seems mpossble for the cross-sectonal area of the tran gets smaller than a certan desgn lmt, and the tunnel cross-secton cannot be expanded further due to the tremendous constructon costs. But accordng to prevous studes, tran aerodynamc performance s also nfluenced by the nose shape. Based on three-dmensonal numercal smulaton, Cho et al. (014) evaluated the aerodynamc effects based on the dfferent the tran nose lengths and the tunnel cross-sectonal areas, t was revealed that the aerodynamc drag n a tunnel can be mnmzed up to around 50% by changng the tran nose type from a blunt to a streamlned shape. Munoz-Panagua et al. (015) performed an optmzaton study of the nose shape of a hgh-speed tran n the open ar usng the adont method, the method was demonstrated to be effectve and a sgnfcant reducton of the aerodynamc drag was amed. By adoptng a newly ntroduced regresson technque, Lee et al. (007) conducted a study on the nose shape desgn of hgh-speed trans to reduce the peak value of mcro pressure wave (MPW), the desgn results showed that approprate optmzaton on nose shape can lower the strength of MPW. In vew of the above studes, there s a need to assess the aerodynamc performance of trans wth dfferent nose shapes passng by each other n a tunnel. Some of the prevous studes pad attenton on the aerodynamc nfluence of tran nose shape n the open ar or on a sngle tran runnng through a tunnel. Others focused on the factors such as the tunnel length, tunnel hood, the blockage rato, the tran speed and other parameters on the aerodynamcs when two opposng movng trans meetng each other nsde a tunnel. However, the nfluence of tran nose shape on the aerodynamcs of two opposng movng trans meetng n a tunnel was not consdered. Therefore, the am of ths work s to utlze a three-dmensonal, compressble, turbulence model to nvestgate the aerodynamc performance of hgh-speed trans wth dfferent nose shapes passng by each other through a tunnel. Assessment s performed by analyzng ther aerodynamc loadng and transent pressure on tran surface and tunnel wall. The results can provde certan gudance for the hgh-speed tran nose shape desgn.. SCENARIO OF NOSE SHAPE FOR HIGH-SPEED TRAIN The nose shape of hgh-speed tran has certan nfluence on ts lateral force, lft, drag and wake (Ikeda et al. 003). Generally, wthn constraned desgn space, the longer streamlne length of a tran, the better aerodynamc performance t has. However, too longer streamlne length may lead to reducton of passenger capacty, thus decreasng ralway operaton effcency. Therefore we should prmarly choose the approprate streamlne length accordng to the desgn speed and runnng condton. Then some proper adustment on the horzontal and longtudnal tran nose profle lnes can be added to mprove the aerodynamc performance further. Based on dfferent nose contours, ths paper desgned four nose shapes by combnng two knds of longtudnal profle lnes (A, B) and two knds of horzontal profle lnes (C, D) as presented n Fg. 1. Fg. shows these four 1376

3 Fg.. Vews of trans wth dfferent nose shapes from dfferent drectons. nose shapes: bulged-broad (A+C), ellpsodal (A+D), flat-broad (B+C), fusform (B+D). Note that the bulged-broad and ellpsodal shapes both have the same longtudnal nose profle lne A whle the flat-broad and fusform shapes both have the same longtudnal nose profle lne B. Smlarly, the horzontal nose profle lne C s appled both for the bulged-broad and flat-broad shapes whle the horzontal nose profle lne D s both appled for fusform and ellpsodal shapes. The other parameters such as streamlne length (9 m), total tran length (01.6 m) all reman the same. In order to accurately smulate the case of tran/tran ntersecton n a tunnel, the tran model adopts 8-car unt, namely the head car, sx mddle cars and the tal car, ncludng the boges and wndshelds, whch s the same as actual condtons. Meanwhle, small obects wth complex structures lke roof pantographs, lghts and handlebars have been omtted to save computng resources. 3. NUMERICAL SIMULATION MODEL 3.1 Mathematcal Model In ths work, the tran speed s 50 km/h and the length of the tunnel s 1000 m. Although the tran speed s less than Mach number 0.3, the space nsde the tunnel s confned by the tunnel wall and tran body, so the ar s supposed to be compressble, namely deal gas. To understand the aerodynamc phenomenon caused by two opposng trans passng by each other through a tunnel, an unsteady, compressble, renormalzaton group (RNG) k-ε turbulence model was appled. The RNG k-ε turbulence model has been recently proved to be effectve to smulate the aerodynamc effects generated by tran/tunnel entry or tran/tran passng by each other n a tunnel (Chu et al. 014; L et al. 016; Nu et al. 017), so t was also adopted n ths work. The governng equatons of the contnuty equaton and RANS equatons are lsted as follows: t x u 0 (1) u u u t u x x x x u u gδ3 u x p x u l - 3 x l () where ρ s the ar densty, p and u are the mean pressure and velocty, μ s the dynamc vscosty of the ar, the subscrpts,,l = 1,, 3, represent the x, y, and z drectons respectvely. The tme-averaged Reynolds stress u u can be expressed as the mean velocty gradents va the Boussnseq hypothess: uu - 3 ρk μ t μ t u u x x u k δ x k (3) k μt ρc μ (4) ε here μ t s the turbulent vscosty and k s the turbulent knetc energy, the model coeffcent C μ = To make the above equatons closed, the turbulent knetc energy and the energy dsspaton rate equatons are presented as follow: ρk t x α x k μ eff ρku k G x ρε ρεu k ρε t x * ε C1ε αε μeff Gk x x k ε Cε ρ k (5) (6) where μ eff s the sum of knetc and turbulent vscostes. α and αk are the recprocal of the 1377

4 Fg. 3. Computatonal doman. Fg. 4. Schematc dagram of the computaton doman and boundary condtons: (a) sde vew; (b) top vew; (c) cross-sectonal vew. turbulent knetc energy and the dsspaton rate, respectvely. Gk s the generated tem of turbulent knetc energy caused by the mean velocty gradent. The model coeffcents C 1ε * and C ε are gven by: * 1 - / 0 C 1ε C1ε - (7) 3 1 1/ k η E E (8) ε E 1 u x u x where C1ε=1.4, Cε=1.68, η0=4.377, β=0.01. (9) The governng equatons above were solved by commercal software Fluent and the computaton doman was dscretzed by the Fnte Volume Method (FVM). Addtonally, the standard wall functon s appled to handle the arflow near wall regon. 3. Computatonal Doman and Boundary Condtons The computatonal doman of the smulaton s demonstrated n Fg. 3 and Fg. 4. The whole computatonal doman conssts of the statonary regon of zone 1 and the sldng regons of zone and zone 3. Zone and zone 3 contans tran A and tran B respectvely whle zone 1 contans the tunnel doman and the outer doman. The outer doman s smulated as two rectangular bodes 1378

5 whch are 600 m n length, 10 m n wdth and 60 m n heght as demonstrated n Fg 4. The dmensons are chosen to guarantee the flow near the tunnel entrance s not affected by outer doman. To realze the relatve moton and data exchange between the trans and the surroundngs, sldng mesh method was utlzed between zone 1/zone, zone 1/zone 3 and zone /zone 3 through pars of grd nterfaces as llustrated n Fg. 4. Unlke dynamc mesh technque whch need mesh regeneraton to realze the relatve movement, by usng sldng mesh method, tran domans of zone 1 and zone can slde relatvely by each another along x-axs wthout mesh regeneraton. The tunnel chosen n ths work s a double-track tunnel whose cross-sectonal area s 80 m, and the blockage rato, whch s the sectonal area of carrage dvded by the tunnel sectonal area, s 14.04%. The tunnel s 1000 m n length and the dstance between the centers of tracks s 4.4 m. The tran s placed n the left sde of the tracks along the tunnel due to the regulaton that the trans of the ralway n Chna are left-sded. The moton of the tran s defned va the userdefned functon (UDF), whch s m/s and m/s for tran A and tran B respectvely. The fxed regon of the tunnel and ground are treated as hexahedral grd. Because of the complex shape of the tran body, sldng regon of the tran domans (zone and zone 3) are dscretzed by more adaptve non-structured grd. Small sze grd s utlzed close to the tran body so as to smulate the boundary layer, the thckness of the frst layer s 1.5 mm and the y+ around the tran surface s nearly 40, whch bascally meets the demands of the RANS model. The surface grd of the tran body and tunnel portal are llustrated n Fg. 5. The total number of the grd elements s about The tme step for unsteady computng s s, whch s suffcent to solve the unsteady flow feld n the tunnel. Commercal software FLUENT s used to smulate the whole tran movement n the tunnel. Because the tran starts n the open feld, the pressure outlet boundary condton s added to the outer doman. As presented n Fg. 4, no-slp wall boundary condtons are utlzed for the tran body, the tunnel wall and the ground. To ensure the stablty of the flow fled when the trans suddenly enter nto the tunnel, the two trans are both placed n 50 m from the tunnel portals. 3.3 Measurng Ponts Layout Due to the symmetrcal case when two opposng movng trans passng by each other through a tunnel, the measurng ponts are set only on one tran s surface. The man purpose of ths paper s focusng on the aerodynamc performance nfluenced by dfferent tran nose shapes. Therefore, more measurng ponts are set on the head and tal car. As demonstrated n Fg. 6, the head car has 7 measurng ponts on the tran surface, and each mddle car has measurng ponts at the symmetrcal locatons. Measurng pont layout on the tal car s the same as the head car, the seral number s dentfed from head to tal successvely. Thus the amount of measurng ponts s 6 n total ( 7+6 =6). The seral numbers n the bracket represent the measurng ponts on the other sde of tran surface, whch s the ntersecton sde as llustrated n Fg. 7(a). Apparently, the seral numbers outsde the bracket represent the measurng ponts of the non-ntersecton sde. To nvestgate the pressure transent nsde the tunnel, 9 measurement ponts are set on the tunnel wall at the heght of 4. m from the ground, whch s shown n Fg. 7(b). Fg. 5. Grd of tran surface and tunnel zone: (a) tran surface; (b) tunnel portal. 4. MODEL VALIDATION In 008, seres of full-scale tests at km/h on tunnel aerodynamcs were carred out n Hefe- Wuhan hgh-speed ralway n Chna. To verfy the calculaton algorthm adopted n the paper, the present model was appled to smulate the full scale test through Yngzush tunnel at the target speed of 13 km/h. The parameters of the trans and the tunnel n the numercal smulaton were the same as the full-scale test. The tran used n the test was CRHA (Fg. 8b), whose length was 01.4 m. The tunnel cross-sectonal area was 9 m wth a length of 1080 m. Pressure transducers produced by Kulte Semconductor Products Corporaton n Amerca were used to montor the pressure varaton on the tran surface, and the range of the transducer was 15 ps. The locaton of two trans passng by each other was at 344 m from the tunnel entrance. The portal of Yngzush tunnel and the test tran were shown n Fg. 8. Two ponts were used to compare the pressure waves obtaned from the full-scale test and the 1379

6 Fg. 6. Measurng pont layout on tran surface. Fg. 7. Measurng pont layout on tunnel wall: (a) cross-sectonal vew; (b) longtudnal vew. Fg. 8. Tunnel and the tran used n the full-scale test: (a) portal of Yngzush tunnel; (b) second car of the CRHA tran wth sensors. Fg. 9. Comparsons between the calculated and expermental results of the tme-pressure hstory on tran surface: (a) No. 6 measurng pont on the head car; (b) No. 8 measurng pont on the second car. numercal smulaton: one pont was on the mddle of the head car (No. 6 pont, refer to Fg. 6), and the other s on the mddle of the second car (No. 8 pont). As ndcated n Fg. 9, the pressure waveforms between the smulaton and the experment showed good agreement wth each other. The peak-to-peak pressure value, whch s the dfference between the postve maxmum pressure and the negatve maxmum pressure, s used to estmate the pressure varaton nsde the tunnel. In Fg. 8(a) the peak-to-peak pressure value of No. 6 pont obtaned from smulaton and feld test was 3098 Pa and 956 Pa respectvely, the error of whch s 4.8%. In Fg. 9(b) the peak-to-peak 1380

7 Dstance from tunnel entrance /m Table 1 Peak-to-peak pressure value on tunnel wall Peak-to-peak pressure value / Pa Bulge-broad Ellpsodal Fusform Maxmum devaton % % % % % % % % % pressure value of No. 8 pont for smulaton and feld test was 963 Pa and 896 Pa respectvely, wth an error of.3%. The largest pressure dfferences were both less than 5%. Therefore the numercal smulaton method adopted n ths paper was relatvely accurate to reflect the aerodynamc effects caused by two opposng trans passng by each other through a tunnel. Addtonally, from the comparsons of these two measurng ponts, t was found that the numercal results were slghtly larger than that of the expermental data. The man reason was assumed that the tran speed nsde the tunnel durng the test was slghtly lower than the target speed due to the actual condtons. 5. RESULTS AND DISCUSSION 5.1 Pressure Transent on Tunnel Wall Table 1 presents the peak-to-peak pressure values at dfferent longtudnal locatons on tunnel wall. As can be seen from the table, due to the propagaton of pressure waves nsde the tunnel, the pressure at dfferent longtudnal locatons on tunnel wall at the same heght vares dfferent, however the nfluencng rules of the pressure generated by trans of the four dfferent nose shapes are almost dentcal. The pressure varaton at the tunnel portals s relatvely low. The largest pressure varatons all occur on the tunnel wall 600 m from the entrance. At the symmetrcal locatons on the tunnel wall n longtudnal drecton, say at 0 m and 980 m from the tunnel entrance, the pressure varatons are nearly dentcal because of the symmetrcal movements of the two opposng trans. Wth the ncrease of the dstance from tunnel entrance, the pressure values rse frstly (entrance to /5 of the tunnel length), afterwards declne and then rse agan (/5 to 3/5 of the tunnel length), fnally declne all the way (3/5 of the tunnel length to ext). Fg. 10 demonstrates the pressure varatons of three typcal locatons nsde the tunnel. The pressure varaton at x=0 m near the tunnel portal s lower because the tran does not fully enter nto the tunnel, and the compresson wave has not fully developed yet. The pressure varaton becomes more sgnfcant further nsde the tunnel such as x=400m and x=500 m due to the nose-entry compresson whch fully has been developed. Generally, the pressure varatons n the tunnel are very complex due to the superposton of reflected waves and passng-by of the trans, the postve maxmum pressure measured on the tunnel wall s nduced by the nose-entry compresson wave whle the negatve maxmum pressure s not only affected by the expanson wave but also nfluenced by the passng-by of the trans (Ko et al. 01). When the tran passes through a certan locaton nsde the tunnel, the surroundng ar wll be drven to move accordngly, the pressure waveforms of x=400 m and x=500 m n Fg.10 have a sudden drop at t=6.5 and t=7.9 s respectvely due to the nose passng-by of tran A. When the nose passng-by encounters the expanson wave of x=400 m at t=6.5 s, the negatve maxmum pressure wll be renforced, however, when the nose passng-by encounters the compressve wave of x=500 m at t=7.9 s, the negatve maxmum pressure wll be reduced accordngly. Whereas the nose-entry nduced maxmum postve pressure of these two ponts are approxmately dentcal. As a result, the peak-topeak pressure at x=500 s lower than that at x=400 m. Among the four nose shapes, the largest pressure varaton s nduced by bulge-broad shape at x=600 m, and the largest devaton reaches 4.7% at x=0 m among the four shapes. Notce that the pressure varatons between bulged-broad and ellpsodal shape, as well as flat-broad and fusform shape are closer to each other whle between these two groups there s relatvely a larger gap. Ths s manly because the two groups both have same longtudnal nose profle lnes. 1381

8 Pressure/kPa t=6.5 s t=7.9 s tran nose passng-by x=0 m x=400 m x=500 m Tme (s) Fg. 10. Tme-pressure hstores of three typcal ponts on the tunnel wall of ellpsodal shape. When a hgh-speed tran suddenly moves nto a tunnel, a compresson wave s nduced and travels through the tunnel at sonc speed, once the compresson wave arrves at the tunnel portal, part of the wave s reflected backwards and part s emtted outsde the tunnel whch leads to boomng nose and vbraton. Such phenomenon s the socalled mcro pressure wave (MPW). The strength of the MPW s largely determned by the peak pressure gradent of the ntal compresson wave (Kkuch et al. 011). Therefore, t s possble to reduce the MPW by dmnsh the pressure gradent of the ntal compresson wave. It s maybe one of the most avalable methods to reduce MPW wth relatvely lower cost by optmzng the nose shape of the tran. The ntal compresson waves of measurng pont No. 1 at x=0 m and No. 5 at x=500 m are shown n Fg. 11. As can be seen, the waveforms of these two measurng ponts are dfferent due to ther dfferent locatons along the tunnel. The dfference of the waveforms among the four nose shapes s more obvous near the tunnel portal but dffers slghtly further nsde the tunnel. The pressure rse of No. 1 pont near the tunnel portal s manly nduced by the tran nose-entry, hence, the nfluence of the tran nose shape s domnant. The No. 5 measurng pont, however, les further nsde the tunnel, the pressure rse s nduced by two factors: one s the nose-entry, the other s the frcton effects of whole tran enterng nto the tunnel, whle the latter s almost not affected by the tran nose shape. Therefore the dfference for dfferent nose shapes s relatvely lower than the No. 1 pont due to superposton results of these two factors. When the pressure begns to rse, the pressure rse steepens more for bulge-broad and ellpsodal shapes than the other two shapes. However, the tme for the pressure to ncrease from zero up to peak value s approxmately the same. The peak pressure values of flat-broad and fusform shapes are also lower than those of bulge-broad and ellpsodal shapes. In Fg. 11(a), compared wth bulge-broad shape, the peak value of the ntal pressure nduced by flat-broad shape s reduced by 5.3%. As mentoned earler, the bulged-broad and ellpsodal shapes, as well as fusform and flatbroad shapes, these two groups both have same longtudnal nose profle lnes. Therefore, ths pattern of pressure dfference can be attrbuted to the change of longtudnal nose profle lne. Furthermore, s was revealed that the horzontal nose profle lne has lttle effect on the varaton of the ntal compresson wave. Pressure/kPa Pressure/kPa (a) Ellpsodal Bulged-broad Fusform Tme/s (b) Ellpsodal Bulged-broad Fusform Tme/s Fg. 11. Intal compresson waves nduced by trans of dfferent nose shapes: (a) No. 1 measurng pont; (b) No. 5 measurng pont. 5. Pressure Transent on Tran Surface Fgure 1 shows the peak-to-peak pressure of each measurng pont on tran surface n longtudnal drecton. The measurng ponts of No. 1 on the nose and No. 6 on the tal are placed n the mddle of the ntersecton sde and non ntersecton sde (refer to Fg. 6). So Fg. 1(a) and Fg. 1(b) both contans these two ponts. The surface pressure on tran body, whether t s ntersecton sde or non ntersecton sde, the devaton of the pressure varatons among the four nose shapes s relatvely large only at nose and tal where the surface curvature change s qute sharp. Whereas the pressure dfference on the mddle cars s rather small. The pressure varatons at nose and tal for trans whch have the same longtudnal nose profle lne are almost dentcal, whle there s sgnfcant dfference for trans whch have dfferent longtudnal nose profle lnes. For nstance, the pressure varatons on tran nose of flat-broad and fusform shape are 501 and 5130 Pa respectvely, they both have the same longtudnal nose profle B. Whle the pressure varaton for bugle-broad and ellpsodal shape are 5510 and 5441 Pa respectvely, they both have the same longtudnal nose profle lne A. Obvously, the tran surface pressure s more nfluenced by the longtudnal nose profle lne than 138

9 horzontal nose profle lne. The pressure varatons on tran surface of longtudnal nose profle lne B are smaller than that of profle lne A. Addtonally, among the four dfferent nose shapes, the hghest pressure mpact s on the tran nose. Whle the pressure varaton decreases along wth tran length drecton, but rse agan at tal. Durng the whole process of the tran movement n the tunnel, the maxmum pressure varaton occurs on the tran nose, the hghest of bulge-broad shape and the lowest of flat-broad shape are 5510 Pa and 501 Pa respectvely, dfference of whch s 9.7%. Pressure/kPa Pressure/kPa (a) Bulge-broad Ellpsodal Fusform Measurng pont number (b) Bulge-broad Ellpsodal Fusform Measurng pont number Fg. 1. Peak-to-peak pressure value on tran surface under dfferent nose shapes: (a) nonntersecton sde; (b) ntersecton sde. 5.3 Analyss of Aerodynamc Drag Fgure 13 presents the total drag of the trans wth dfferent nose shapes passng by each other through the tunnel. EN ndcates the moment when the head car enters the tunnel, NN represents the moment when two trans nose meet each other; NT refers to the exact moment when the two trans are paralleled sde by sde; TT means the moment when the two trans tal meet each other. EX stands for the moment when the head car exts the tunnel. As can be seen, the total drag varatons of the trans wth dfferent nose shapes are bascally the same, the pressure values are all postve, only slghtly dfferent n ampltude. Fg. 14 shows the tmepressure varaton of No. 1 measurng pont on tran nose. The varatons of the waveforms between Fg. 13 and Fg. 14 show smlar trends, t s ndcated that the total drag s hghly correlated wth the pressure varaton on tran nose. Total drag/kn EN NN NT TT EX 80 1 Bulge-broad Ellpsodal Fusform Tme/s Fg. 13. Total drag of trans wth dfferent nose shapes. Pressure/kPa EN Ellpsodal Fusform Bulge-broad NN NT TT Tme/s Fg. 14. Tme-pressure varaton of No. 1 measurng pont on tran nose. Due to the confne space of the tunnel wall, when the head car suddenly enters nto the tunnel at ten=0.7 s, the ar n front of the tran s nose s densely compressed, producng compresson waves smultaneously n both opposte drectons, the total drag rses perpendcularly accordngly. When the tran moves further nto the tunnel from nose to tal, the compressed ar releases backwards along the annular space between the tran and tunnel, thus the compresson effects of the ar become weaker than before, and the drag ncreases gradually. Once the tran fully enters nto the tunnel, an expanson wave s formed, leadng to a vacuum regon at the tunnel entrance, so the drag rses dramatcally and reaches the peak at t=4. s due to the sucton force of the vacuum regon. At tnn =7.9 s, the drag has a pulse change due to the compressed ar from both ends meet each other and rapdly release along the gap between the two trans. When the two trans passed each other after the NN moment, the drag decreases and hts the lowest value at the tnt=9.3 s. Although the drag ncreases after the NT moment, the maxmum value s stll lower than that peak value before two trans meet (t=4. s), ths s resulted from the dmnuton of reflected compresson waves. The drag fluctuates and vares all the way through the tunnel due to the passng-by of the opposte tran and successve propagatons and reflectons of the pressure waves. Untl at tex=15.1 s, the drag frstly ncreases then gradually decreases and fnally gets out of the nfluence of the tunnel pressure waves. The total drag expands from small 4 3 EX 1383

10 to large by the sequence of fusform, flat-broad, ellpsodal, bulge-broad shape. The maxmum drag of bulge-broad shape and the mnmum of fusform shape are 79.9 kn and 74.3 kn respectvely. The largest dfference of the total drag attans 7.4% due to the change of nose shape. To analyse the nfluencng rules of the nose shapes on aerodynamc drag more ntutvely, the maxmum drag of trans wth dfferent nose shapes are shown n Table. Due to the smlar aerodynamc characterstcs of the mddles cars, the 3rd car s chosen to represent the mddle cars. As can be seen, the nose shape has largest mpact on the tal car drag, smallest mpact on the mddle car drag, the largest drag devaton on the tal car dffers 16.96%. Whether t s head car, mddle car or tal car, the sequence of the drag from small to large s fusform, followed by flat-broad, ellpsodal, bulge-broad. Table Maxmum drag of trans wth dfferent nose shapes Nose shape Head car Mddle car Tal car Bulge-broad Ellpsodal Fusform Devaton 5.% 3.51% 16.96% Fg. 15. Velocty contours around trans of dfferent longtudnal nose profle lnes: (a) head car of profle lne A; (b) head car of profle lne B; (c) tal car of profle lne A; (d) tal car of profle lne B. By the reason that the fusform and flat-broad shapes both have the same longtudnal nose profle lne B, the profle lne change of these two shapes are smoother and more fluent than the other two shapes, so the arflow s not easly blocked and separated. Fg. 15 presents the velocty contours around trans wth dfferent longtudnal nose profle lnes at t=4.5 s n the tunnel. Compared wth Fg. 15(a), the dstrbuton of the arflow velocty n Fg. 15(b) at the transton regon A (.e. from the nose to tran body) s more average and gradual, so the pressure n front of the tran nose s reduced accordngly. Smlarly, although n Fg. 15(d) the arflow around the tal car of profle lne B separates earler than the tal car of profle lne A n Fg. 15(c), but the velocty change s not that steep or abrupt. Consequently, the negatve pressure at tal regon s much lower and average. The pressure dfference between the nose and tal s thus decreased. Hence, the pressure drag s reduced between the nose and tal. It can be concluded that the aerodynamc drag characterstcs for the trans of the longtudnal nose profle lne B s relatvely better. 5.4 Analyss of Lateral Force. Fgure 16 presents the tme-hstory of the head car lateral force of the four nose shapes, when the tran enters nto the tunnel at t=ten, the lateral force fluctuates wth a sudden change of ar pressure n the tunnel. When the tran s entrely runnng nsde the tunnel between the EN and the NN moment, as well as the NT and the EX moment followed, the lateral force appears to be slghtly negatve and reman almost constant. Ths s manly because the flow feld nsde the double-track tunnel s unsymmetrcal and the negatve pressure on the tran surface closer to the tunnel wall sde (nonntersecton sde) s greater, hence, a negatve lateral force appears to slghtly push the tran towards the tunnel wall. When the two trans meet each other at t=tnn, the hgh pressure regon around the tran noses push the head cars laterally away from each other. As a result, the lateral force has a pulse change, frst negatve and then postve. Between the moment of the NN and the NT, due to passng by the opposte tran s wndshelds, the compressed ar between the two trans gap successvely releases towards the wndsheld ntervals for several tmes. Consequently, the lateral force has several obvous fluctuatons. Once the opposte tran s tal passes by at t=tnt, the lateral force has another pulse change smlar to that of the NN moment. When the head car leaves the tunnel at t=tex, the boundary condton suddenly changed nto the open feld from the confned arspace nsde the tunnel, an expanson wave s generated and spreads along the tunnel and causes the pressure drop. As mentoned n Secton 3., the tran s runnng on the left sde of the track, the non-ntersecton sde s much narrower, so the flow feld s not symmetrcal, the pressure on the tran body closer the tunnel wall decreases more, therefore, the fluctuatons of the lateral force are observed at t=tex. When the tran completely leaves the tunnel, the lateral force s not nfluenced by the tunnel anymore and regan to zero. From the perspectve of peak-to-peak value of the lateral force, the lateral force at the NN moment s hgher than that of the NT moment, addtonally, the lateral force s more 1384

11 nfluenced at the EX moment than that of the EN moment. In order to analyse the dfference of lateral force of the trans under dfferent nose shapes, the peak-topeak lateral force of each car of these four shapes are presented n Fg. 17. As can be seen, the lateral force actng on the head car and tal car s qute hgher, whle the sx mddle cars are relatvely lower. Moreover, t can be deduced that the lateral force characterstcs s more nfluenced by longtudnal nose profle lne. For on the same condtons, lateral force of trans wth the longtudnal nose profle lne B (.e. fusform, flat broad shape) are relatvely lower. The nfluencng rules on lateral force of the head car, tal car and sx mddle cars are dentcal. The sequence from small to large s flat-broad, fusform, bulge-broad, ellpsodal shape. The nose shape has sgnfcant dfference of lateral force on the tal car, the maxmum devaton attans 31.5%. Lateral force/kn EN Ellpsodal Bulge-broad Fusform NN NT Tme/s Fg. 16. Tme-hstory of lateral force of the head car under the four nose shapes. Lateral force/kn EX Fusform Ellpsodal Bulge-broad Car number Fg. 17. Peak-to-peak lateral force of the each car of trans wth dfferent nose shapes. 6. CONCLUSIONS The turbulent flow around the trans of dfferent nose shapes passng by each other through a tunnel were computed usng three dmensonal, compressble, RNG k turbulence model to uncover the aerodynamc performance. The numercal model was valdated by comparng wth the feld measurement results. Then, the model was used to examne the transent pressure and aerodynamc loadngs caused by opposng trans of dfferent nose shapes passng by each other through a tunnel. The results of the study are summarzed as follows: 1) In the whole process of the two opposng trans passng by each other n a tunnel at 50 km/h, the nose shape has less nfluence on the tunnel wall pressure at the same locaton from the tunnel entry, the maxmum devaton s 4.7%; surface pressure on the head and tal car s more nfluenced by the nose shape whle mddle cars are less nfluenced, the maxmum devaton of pressure varaton on trans among dfferent nose shapes occurs on the tran nose, the dfference s about 9.7%. ) The aerodynamc drag s decreased by the sequence of bulge-broad, ellpsodal, flat-broad, fusform shape. Compared wth bulge-broad shape, the total drag of fusform shape s reduced by 7.4%. Lateral force gradually decreases by the sequence of ellpsodal, followed by bulge-broad, fusform, flatbroad shape, the maxmum devaton on the tal car attans 31.5% due to the change of nose shape. 3) Aerodynamc performance of two opposng trans passng by each other n a tunnel s lttle nfluenced by the horzontal nose profle lne, but s more nfluenced by the longtudnal nose profle lne. The aerodynamc performance for trans wth the longtudnal nose profle lne B (.e. fusform, flat-broad shape) s relatvely better when passng by each other through a tunnel. ACKNOWLEDGEMENTS Ths research was supported by Central South Unversty Innovaton-drven Plan (015CX003), Central South Unversty Independent Exploraton and Innovaton-drven Proect (017zzts588), Natonal Natural Scence Foundaton of Chna ( ), Natonal Key Research and Development Plan (016YFB100504), Technologcal Research and Development Program of Chna Ralways Corporaton (016T004-B, 016T004-D), Central South Unversty Teachers Research Fund (013JSJJ014). REFERENCES Cho J. K. and K. H. Km (014). Effects of nose shape and tunnel cross-sectonal area on aerodynamc drag of tran travelng n tunnels. Tunnellng & Underground Space Technology, 41, Chu, C. R., S. Y. Chen, C. Y. Wang and T. R. Wu (014). Numercal smulaton of two trans ntersectng n a tunnel. Tunnellng & Underground Space Technology 4(5), Fu, K. and T. Ogawa (1995). Aerodynamcs of hgh speed trans passng by each other. Computers and Fluds 4(8), Glbert, T., C. J. Baker and A. Qunn (013). Gusts caused by hgh-speed trans n confned spaces 1385

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