Reasonable compensation coefficient of maximum gradient in long railway tunnels

Transcription

1 Journal of Modern Transporaion Volume 9 Number March 0 Page -8 Journal homepage: jm.swju.edu.cn DOI: 0.007/BF Reasonable compensaion coefficien of maximum gradien in long railway unnels Sirong YI * Liangao NIE Yanheng CHEN Fangfang QIN School of Civil Engineering MOE Key Laboraory of High-Speed Railway Engineering Souhwes Jiaoong Universiy Chengdu 6003 China Absrac: This paper deals wih he heory and calculaion mehods for compensaion of he gradien in railway unnels hrough heoreical analysis numerical calculaion and saisic regression mehods. On he basis of he principle ha he resulan force is zero he formula of he maximum calculaed gradien was derived for he freigh and passenger line and high-speed passenger special line. The formula of aerodynamic drag in unnel is provided using he domesic and foreign relevan experimenal invesigaions and revised wih modern rain and engineering parameers. A calculaion model of aerodynamic drag when he rain goes hrough a single-racked unnel was buil. Finally he concep of maximum calculaed gradien was adoped o revise he formula for compensaion of he gradien in railway unnels. Key words: railway unnel; maximum gradien; profile; gradien compensaion 0 JMT. All righs reserved.. Inroducion F or freigh and passenger lines a he locaion where he maximum gradien needs o be used in design when he rain passes hrough a unnel of lengh more han 400 m is addiional resisance increases bu he adhesion coefficien lessens which leads o he design gradien of he profile plus he equivalen gradien of addiional aerodynamic drag in he unnel being greaer han he maximum gradien. Therefore in he profile design we need o compensae for he maximum gradien o ensure he general freigh rain can pass hrough his locaion a no less han he sipulaed speed. Code for Design of Railway Line (hereinafer referred o as he Line Specificaion) offers us he maximum gradien compensaion coefficiens for he corresponding unnels []. However due o he advancemen of railway speed in China he calculaion formula in he exising codes canno be adaped o he curren engineering condiions. In order o revise he principle and parameers of maximum gradien compensaion for railway unnels we should combine new echnical condiions of he railway sysem o sudy he heory mehod and compensaion model. Considering he elecric railway his paper will inroduce he research achievemen on developing a rea- Received Dec.6 00; revision acceped Jan. 0 * Corresponding auhor. sryi@home.swju.edu.cn doi: /j.issn X sonable compensaion coefficien for he gradien of a long railway unnel.. Calculaion model of maximum gradien of design line The maximum calculaed gradien of a railway line is defined as he gradien value of he consecuive ascending grade on which a given locomoive can haul he rain wih a specified weigh a he calculaed consan speed of he locomoive. For freigh rains and passenger rains wih racion mass of G he maximum calculaed gradien of he rain is derived based on he principle ha he resulan force acing on he rain is zero when he freigh rain runs on a consecuive ascending grade a he specified calculaed consan speed of he locomoive. For a provided racion mass norm he maximum calculaed gradien a he secion where he rain is hauled by a single locomoive can be calculaed as follows []: i cmax ufc ( Pw 0 Gw 0) g ( P G) g where G is he norm of racion mass in ; i cmax is he maximum calculaed gradien; w 0 is uni basic resisance of locomoive under he calculaed speed in ; w 0 is uni basic resisance of rolling sock under he calculaed speed in ; F c is calculaed racion force in kn; P is locomoive mass in ; u is uilizaion coef-

2 Journal of Modern Transporaion 0 9(): -8 3 ficien of racion force; g is acceleraion of graviy in DOI: m/s 0.007/BF A he secion where he maximum gradien needs o be used if he equivalen gradien of he profile exceeds he maximum gradien he freigh rain will evenually run a a speed less han calculaed speed on he consecuive ascending grade which will resul in accidens due o he slow speed even causing a suspension. Hence he design gradien of he profile plus he equivalen gradien of addiional resisance in he unnel should no be greaer han he maximum gradien. Therefore for he profile design of railway we need o reduce he maximum gradien o ensure he freigh rain passes hrough his secion a no less han calculaed or sipulaed speed... Calculaion model of addiional aerodynamic drag in single-racked unnel When a rain goes hrough a double-rack unnel here is no direcional airflow so he average aerodynamic drag formula canno be deduced heoreically. In he case of no meeing rains because he rain runs hrough he unnel of larger cross secion he blockage raio becomes greaer and he aerodynamic drag is less han ha in he single-rack unnel. In he case of meeing rains in double-rack unnel hrough mahemaical analysis on he energy and momenum of aerodynamic drag we can analyze he flow field (velociy field and dynamic pressure field) around he locaion of he meeing rains of differen ype and lengh wih differen speed and hen calculae he incremen of aerodynamic drag. The paper herein deals wih a calculaion mehod of addiional aerodynamic drag in single-racked unnel. When a rain goes hrough a single-racked unnel here exiss direcional airflow in unnel. Then we can deduce average aerodynamic drag formula heoreically. Air canno spread due o being resrained by unnel when rain is running in unnel leading he pison phenomenon i.e. he difference beween head posiive pressure and ail negaive pressure which produces he resisance o he rain. Meanwhile he urbulen flow in unnel produces fricion beween he air and he surface of he rain and he unnel which also generaes he resisance o he rain. Therefore when he rain is running in he unnel aerodynamic drag acing on he rain is far more han ha in he open. The aerodynamic drag incremen is called addiional aerodynamic drag in he unnel. In he calculaion of aerodynamic drag incremen in he unnel a series of parameers need o be deermined firs such as he fricional resisance coefficien of he rain surface fricional resisance coefficien of unnel surface he pressure drag coefficien of he rain head and ail rain shape parameers and unnel design parameers. These calculaion parameers deermine he correcness of he resul. Especially he pressure drag coefficien of he rain head and ail and he fricional resisance coefficien of he rain surface have a grea influence on he correcness of he resul. When a rain is going hrough a unnel he aerodynamic drag includes hree iems: pressure drag of he rain head pressure drag of he ail and surface fricion resisance of he body. The key o deermining aerodynamic drag when a rain passes hrough a unnel is o deermine he pressure drag coefficien of he rain head and ail surface fricion resisance coefficien of he rain body and wind speed in he unnel. The relaed sudies [3-5] show ha addiional aerodynamic drag in he unnel is relaed o driving speed lengh of he rain he superficial area of he rain agains he air rain shape unnel lengh area of unnel cross-secion and unnel surface roughness. The relaion beween aerodynamic drag in he unnel air pressure difference and unnel cross-secion area can be expressed as follows: W hf where F is he area of unnel cross-secion for he simplificaion of calculaion can be aken as he value in Table. Table The minimum effecive area of cross-secion in unnel (recommended value in calculaion) m Design running speed of passenger rain (km/h) Elecric racion Doublerack Diesel Tracion Singlerack Singlerack Doublerack Remarks Wihou considering requiremens of double-decked conainer rains Uni aerodynamic drag in he unnel is hf w ( P G) g where h is uni difference of air pressure in N/m : h K ( vv0 ) where K is he effec coefficien of pison pressure: 4 NLr 860 Lr K ( F / F ) ( F / F) r r

3 4 Sirong YI e al. / Reasonable compensaion coefficien of maximum gradien in long railway unnels where L r is lengh of rain in m and F r is area of crosssecion of rain aken as.6 m ; is he densiy of air DOI: 0.007/BF aken as. kg/m 3 ; v is speed of rain in m/s; v 0 is wind speed in pison in m/s: v v0 / K where is oal resisance coefficien of unnel: L Lr d where is he sum of par resisance coefficien a he enrances o he unnel aken as.5; is inernal fricion coefficien in he unnel aken as 0.05; L is lengh of he unnel in m; d in m is equivalen diameer of he unnel: han 60 km/h i is aken as.5 m for single-rack unnel and 3.55 m for a double-rack unnel. When design speed is in he range of 60 o 00 km/h i is aken as 34.5 m for a double-rack unnel. When design speed is in range of 00 o 50 km/h i is 8.0 m for a singlerack unnel and 35.0 m for a double-rack unnel. When design speed is in he range of 50 o 350 km/h i is 3.0 m for a single-rack unnel and 37.5 m for a doublerack unnel. Afer subsiuion of he above parameers he oal resisance coefficien in he unnel is L Lr L Lr d 4 F / R According o he above parameers he calculaion formula of uni air pressure difference can be deduced as follows. d 4 F / R where R is unnel perimeer. When design speed is less h K ( vv0 ) 0.05 Kv ( ) 0.5Kv / K L L r ( ) / K 4 F / R Lr 0.5 v ( Fr / F ) L L r ( ) / ( Lr / ( Fr / F ) ) 4 F / R LV r ( Fr / F ) L L r ( ) / ( Lr / ( Fr / F ) ) 4 F / R The formula of he uni aerodynamic drag in a unnel is hf F LrV w ( PG) g ( F r / F ) ( PG) ( Fr / F ) (74.49( Fr / F ).907 ( L Lr )) / L r 4 F / R ALr V ( P G) BC( L Lr) L r where F A ( F / F) B F F C r 74.49( r / ) r.907. ( F / F) 4 F / R.. Maximum calculaed gradien of he unnel secion A he unnel secion where he maximum gradien is fully used when he rain goes hrough he unnel if he calculaed gradien of locomoive approaches he ruling gradien of he design line he gradien equivalen o addiional resisance should be deduced o ensure he

4 Journal of Modern Transporaion 0 9(): -8 5 rain passes hrough his unnel wih no less han he DOI: 0.007/BF calculaed speed of he locomoive. Only he addiional aerodynamic drag in he unnel affecs he compensaion of maximum gradien for he unnel when using elecric racion. For diesel-racion however no only he addiional unnel aerodynamic drag bu also he speed of rain hrough he unnel influences he compensaion of maximum gradien. Le he compensaion of maximum gradien in he unnel be i. Then he maximum design gradien of unnel i ( ) is i i i. max In order o simplify he calculaion he maximum gradien compensaion value for he unnel i can be convered o maximum gradien coefficien. The relaionship of wih design grade i is as follows: i i imax i imax imax. imax For elecric racion w ( i i ) i w ic imax w. c max c ic imax w imax imax For diesel-racion w ( iv imax) iv w i v i max w i max imax iv imax w where w is addiional aerodynamic drag in unnel in ; i max is maximum gradien of design line ( ); i c is calculaed gradien of locomoive namely he gradien value when he rain runs a a consan speed (for he freigh rain i refers o he equilibrium gradien when he locomoive runs a a minimum calculaed speed ( )); i v is he equilibrium gradien under he rain speed hrough he unnel and i equals he uni resulan force value under he rain speed hrough he unnel i.e. i v =fw 0 where f is uni racion force and w 0 is he uni basic resisance. 3. Maximum calculaed gradien in brigh line secion (ouside of unnel) 3.. Relaionship beween racion mass and calculaed gradien for several ypes of freigh locomoives According o he calculaion he relaionship beween racion mass and calculaed gradien for several ypes of freigh locomoives (SS SS3 SS4 SS7 6K 8G) is shown in Fig.. The relaionship is decreasing quinic funcion; namely he adaped calculaed gradien decreases by quinic funcion wih he increase in he racion mass. Calculaed gradien ( ) SS SS3 SS4 SS7 6K 8G Tracion mass G ( 0 3 ) Fig. The relaionship beween racion mass and calculaed gradien for six ypes of locomoives 3.. Surplus value of racion power of elecric locomoive for ruling gradiens For he railway of freigh and passenger lines hauled by elecric locomoive in our counry he ruling gradien should no be greaer han values in Table. Classificaion of railways Table Maximum ruling gradien value Terrain ype Plain Hilly land Mounainous area A presen mos of railways for freigh rains and passenger rains in China employ he ruling gradien of 6 9 or. The surplus of racion force of elecric locomoive on he corresponding ruling grade is shown in Table 3 where i r is ruling gradien Comprehensive analysis of dynamic characerisics for a freigh rain running on ascending grade Table 3 shows ha for freigh rain and passenger rain using locomoives SS4 SS7 8K and 6G when racion mass are 800 and 000 rains can run on he grade wih he ruling gradien of no more han 5 a cerain acceleraed speed. When racion mass is 800 he acceleraed allowance of locomoive SS4 is greaer han he maximum compensaion of gradien in he un-

5 6 Sirong YI e al. / Reasonable compensaion coefficien of maximum gradien in long railway unnels DOI: 0.007/BF Table 3 Surplus of racion force of elecric locomoive on ruling grade Locomoive ype 800 /5 000 /5 800 / 000 / 500 /9 Tracion mass/ruling gradien 800 / / /4 SS SS SS SS K G for 400<L < for 000< L < for 400< L < 000. for 000<L < for 400< L < for 400<L < for 400< L < for 000< L <4 000 (- )i r 0.9 for 000<L < for 000< L < for 4 000< L.8 for 4000< L.35 for 4 000< L 0.9 for 4 000< L 0.6 for 4 000< L nel. In he railway of plain and hilly regions in he case of locomoives SS and SS3 a 800/ 500/ and (railing load/ruling gradien) he calculaed gradien is greaer han he corresponding ruling gradien and he locomoives run a he calculaed speed wih a cerain acceleraion allowance. In he remaining calculaion condiions excep for he allowance is always less han he corresponding compensaion of gradien in unnel in he curren Line Specificaions []. Hence when using elecric locomoives SS and SS3 we should ake he compensaion of maximum gradien in he unnel ino consideraion o ensure ha he locomoive hauls he rain wih no less han he calculaed speed hrough his unnel. When he racion mass is on he grade wih 6 gradien rain can run a he calculaed consan speed of he locomoive wih a cerain acceleraion allowance bu he allowance is less han he compensaion of gradien in unnel. When racion mass is less han in he case of locomoives SS4 SS7 6K and 8G running on he grade wih gradien of 6 9 and calculaed gradien are all more han he ruling gradien and he racion force is surplus. The above analysis shows ha for differen ruling gradien and corresponding racion mass we can ensure he locomoive hauls he rain o run wih cerain acceleraion allowance on limiing ascending grade by properly choosing elecric locomoive. For high-power elecric locomoives SS4 SS7 6K 8G ec. according o he curren Line Specificaions even in a unnel secion locomoives sill are able o pass hrough a no less han he calculaed speed wih cerain acceleraion allowance. 4. Model of relaionship beween aerodynamic drag in unnel and rain speed When rains wih he same racion mass pass hrough unnels wih he same lengh aerodynamic drag in unnel is in direc proporion o he square of rain speed. As he lengh difference among differen ypes of locomoives is iny aerodynamic drags in a unnel are very close ending o he same quadraic curve. Therefore when he norm of racion mass is cerain he aerodynamic drag in a unnel can be regressed o he uniform calculaion formula. Table 4 provides he relaionship of he aerodynamic drag in a unnel and he speed (V) of he rain wih racion mass of Table 4 General formula of aerodynamic drag of elecric racion freigh rain wih racion mass in unnel L (m) 000 w =0.55V V w =.66V V w =.65V V w =.63V V w =.89V V w =3.088V V w =3.45V V Maximum aerodynamic drag in unnel According o Table 4 we can calculae he aerodynamic drag for differen elecric locomoive when i w

6 Journal of Modern Transporaion 0 9(): -8 7 passes hrough he unnel a he calculaed speed. Table 5 shows he aerodynamic drag in a unnel when lo- DOI: 0.007/BF comoives SS4 and SS7 haul rains hrough he unnel wih differen lengh. 6. Comprehensive analysis 6.. Comparison beween calculaed gradien and aerodynamic drag in unnel According o above analysis Table 6 shows he relaionship beween acceleraion allowance and aerody- namic drag in a unnel when he elecric locomoives run wih calculaed speed on ruling grade. Comprehensive analysis for Tables 5 and 6 and Fig. shows ha when using locomoives SS4 SS7 8K and 6G and racion mass is 800 or 000 he rains could run on he grade wih he ruling gradien of no more han 5 a cerain acceleraedspeed. When racion mass is 800 acceleraion allowance of locomoive SS4 is greaer han he maximum compensaion of gradien in he unnel. For he railway in plain and hilly in he case of locomoives SS and SS3 a 800/ 500/ and he calculaed gradien is Table 5 Aerodynamic drag in a unnel when an elecric racion freigh rain passes hrough a he calculaed speed L (m) Locomoive ype G () Passenger rain SS SS SS SS SS SS SS SS SS S SS SS SS SS Locomoive ype Table 6 Comparison beween surplus value of racion force and aerodynamic drag in a unnel when he elecric locomoive runs on ruling grade Tracion mass/ruling gradien 3 000/ / / /4 SS SS SS SS K G W 0.0 for 400< L < for 00< L < for 5 00< L < for 0 00< L < for 5 00< L < for 0 00< L < for 5 00< L <30 000

7 8 Sirong YI e al. / Reasonable compensaion coefficien of maximum gradien in long railway unnels greaer han he corresponding ruling gradien and he DOI: 0.007/BF locomoives run a calculaed speed wih a cerain acceleraion allowance. However in he res calculaion condiions excep for he allowance is always less han he gradien compensaion for corresponding unnel in he curren Line Specificaions. For example when using elecric locomoives SS SS3 we should ake he compensaion of maximum gradien in he unnel ino consideraion o ensure ha he locomoive hauls rain wih no less han calculaed speed hrough his unnel. When racion mass is rain can run on 6 grade a he calculaed speed of locomoive consanly wih a cerain acceleraion allowance bu he allowance is less han he compensaion of gradien in unnel. When racion mass is less han and using locomoives SS4 SS7 6K and 8G o haul rain on he ruling grade of 6 9 and he calculaed gradien is more han he ruling gradien and he allowance is greaer han he equivalen gradien of he aerodynamic drag in he unnel. 6.. Comparison beween calculaed aerodynamic drag and compensaion of gradien in a unnel in curren Line Specificaions Table 7 shows he compensaion of gradien in unnel in curren Line Specificaions and he calculaed aerodynamic drag in unnel. The comparison of he calculaed value wih compensaion value in curren line specificaions shows ha for he elecric racion lines wih he ruling gradiens of 6 9 and when he unnel lengh is less han m calculaed value is no more han he aerodynamic drag in he unnel when L >4 000 m ha is sipulaed in he curren Line Specificaions. Table 7 Comparison beween calculaed aerodynamic drag and compensaion for gradien in a unnel in curren Line Specificaions Ruling Lengh of unnel (m) gradien ( ) 400<L <L4 000 L > Calculaed aerodynamic drag L : 0.90; L : Conclusions () For he differen ruling gradien and racion mass we can properly choose he locomoive from he curren elecric racion locomoives in China o ensure he locomoive hauls rain o run on limiing ascending grade wih cerain acceleraion allowance. The high-power elecric locomoives SS4 SS7 6K 8G ec. even in unnel locaion sill run a no less han he calculaed speed wih cerain acceleraion allowance hrough he unnel. () In he elecric racion railway for freigh and passenger lines when passenger rain is passing unnel locomoive racion allowance is greaer han he incremen of aerodynamic drag in unnel. Therefore he design of maximum gradien of unnel is no affeced by he passenger rain. (3) In he design of railway for freigh rain and passenger rain he influence of aerodynamic drag should be aken ino accoun when a fas-speed passenger rain passes hrough a unnel. The calculaion resuls of his paper show ha when rains have he same lengh and ouside shape for he same ype of locomoive if he racion mass is less he uni aerodynamic drag is greaer. For he same racion mass if he calculaed speed is greaer he aerodynamic drag in unnel is greaer. For elecrical freigh locomoive he calculaed speed of locomoive SS4 is he greaes i.e. 5. km/h and accordingly is aerodynamic drag in unnel is he greaes. According o he above analysis for elecric racion calculaion of aerodynamic drag in unnel can be divided ino seven grades: and he corresponding addiional aerodynamic drag can be calculaed in erms of and 0.95 respecively. References [] The Minisry of Railway of he People s Republic of China Code for Design of Railway Line Beijing: China Planning Press 006. [] S.R. Yi Railway Locaion Design (he hird version) Chengdu: Souhwes Jiaoong Universiy Press 009. [3] Y. Hao Railway Locaion Design Beijing: China Railway Publishing House 978. [4] C.J. Baker S. Dalley J. Johnson e al. The slipsream and wake of a high-speed rain Proceedings of he Insiuion of Mechanical Engineers Par F: Journal of Rail and Rapid Transi 00 5(): [5] H.Q. Tian Train Aerodynamics Beijing: China Railway Publishing House 007. (Edior: Dongju CHEN)