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Reasonable Compensation Coefficient of Maximum Gradient in Long Railway Tunnels

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Reasonable Compensation Coefficient of Maximum Gradient in Long Railway Tunnels Journal of Modern Transportation 1 Volume 19, Number 1, March 2011, Page 12-18 Journal homepage: jmt.swjtu.edu.cn DOI: 10.1007/BF03325735 Reasonable compensation coefficient of maximum gradient in long railway tunnels Sirong YI*, Liangtao NIE, Yanheng CHEN, Fangfang QIN School of Civil Engineering, MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China Abstract: This paper deals with the theory and calculation methods for compensation of the gradient in railway tunnels through theoretical analysis, numerical calculation, and statistic regression methods. On the basis of the principle that the resultant force is zero, the formula of the maximum calculated gradient was derived for the freight and passenger line and high-speed passenger special line. The formula of aerodynamic drag in tunnel is provided using the domestic and foreign relevant experimental investigations, and revised with modern train and engineering parameters. A calcula- tion model of aerodynamic drag when the train goes through a single-tracked tunnel was built. Finally, the concept of maximum calculated gradient was adopted to revise the formula for compensation of the gradient in railway tunnels. Key words: railway tunnel; maximum gradient; profile; gradient compensation © 2011 JMT. All rights reserved. 1. Introduction sonable compensation coefficient for the gradient of a long railway tunnel. or freight and passenger lines, at the location where F the maximum gradient needs to be used in design, 2. Calculation model of maximum gradient when the train passes through a tunnel of length more of design line than 400 m, its additional resistance increases, but the adhesion coefficient lessens, which leads to the design The maximum calculated gradient of a railway line is gradient of the profile plus the equivalent gradient of defined as the gradient value of the consecutive ascend- additional aerodynamic drag in the tunnel being greater ing grade on which a given locomotive can haul the than the maximum gradient. Therefore, in the profile de- train with a specified weight at the calculated, constant sign, we need to compensate for the maximum gradient speed of the locomotive. to ensure the general freight train can pass through this For freight trains and passenger trains with traction location at no less than the stipulated speed. Code for mass of G, the maximum calculated gradient of the train Design of Railway Line (hereinafter referred to as the is derived based on the principle that the resultant force Line Specification) offers us the maximum gradient acting on the train is zero when the freight train runs on compensation coefficients for the corresponding tunnels a consecutive ascending grade at the specified calculated, [1]. However, due to the advancement of railway speed constant speed of the locomotive. For a provided trac- in China, the calculation formula in the existing codes tion mass norm, the maximum calculated gradient at the cannot be adapted to the current engineering conditions. section where the train is hauled by a single locomotive In order to revise the principle and parameters of maxi- can be calculated as follows [2]: mum gradient compensation for railway tunnels, we O F ()Pwc Gwcc g should combine new technical conditions of the railway uc 0 0 icmax , system to study the theory, method, and compensation ()PGg model. where G is the norm of traction mass, in t; icmax is the Considering the electric railway, this paper will in- maximum calculated gradient; w0Ąis unit basic resis- troduce the research achievement on developing a rea- tance of locomotive under the calculated speed, in N/kN; w0ąis unit basic resistance of rolling stock under the calculated speed, in N/kN; F is calculated traction force, Received Dec.16, 2010; revision accepted Jan.11, 2011 c *Corresponding author. E-mail: [email protected] in kN; P is locomotive mass, in t; ¬u is utilization coef- doi: 10.3969/j.issn.2095-087X.2011.01.003 Journal of Modern Transportation 2011 19(1): 12-18 13 ficient of traction force; g is acceleration of gravity, in and tail, train shape parameters, and tunnel design pa- DOI:m/s2. 10.1007/BF03325733 rameters. These calculation parameters determine the At the section where the maximum gradient needs to correctness of the result. Especially, the pressure drag be used, if the equivalent gradient of the profile exceeds coefficient of the train head and tail and the frictional the maximum gradient, the freight train will eventually resistance coefficient of the train surface have a great in- run at a speed less than calculated speed on the consecu- fluence on the correctness of the result. tive ascending grade, which will result in accidents due When a train is going through a tunnel, the aerody- to the slow speed, even causing a suspension. Hence, the namic drag includes three items: pressure drag of the design gradient of the profile plus the equivalent gradi- train head, pressure drag of the tail, and surface friction ent of additional resistance in the tunnel should not be resistance of the body. The key to determining aerody- greater than the maximum gradient. Therefore, for the namic drag when a train passes through a tunnel is to de- profile design of railway, we need to reduce the maxi- termine the pressure drag coefficient of the train head mum gradient to ensure the freight train passes through and tail, surface friction resistance coefficient of the this section at no less than calculated or stipulated speed. train body and wind speed in the tunnel. The related studies [3-5] show that additional aero- 2.1. Calculation model of additional aerodynamic drag dynamic drag in the tunnel is related to driving speed, in single-tracked tunnel length of the train, the superficial area of the train against the air, train shape, tunnel length, area of tunnel When a train goes through a double-track tunnel, cross-section, and tunnel surface roughness. The relation there is no directional airflow, so the average aerody- between aerodynamic drag in the tunnel, air pressure namic drag formula cannot be deduced theoretically. In difference and tunnel cross-section area can be ex- the case of no meeting trains, because the train runs pressed as follows: through the tunnel of larger cross section, the blockage WhFtt , ratio becomes greater, and the aerodynamic drag is less where Ft is the area of tunnel cross-section, for the sim- than that in the single-track tunnel. In the case of meet- plification of calculation, can be taken as the value in ing trains in double-track tunnel, through mathematical Table 1. analysis on the energy and momentum of aerodynamic drag, we can analyze the flow field (velocity field and Table 1 The minimum effective area of cross-section in 2 dynamic pressure field) around the location of the meet- tunnel (recommended value in calculation) m ing trains of different type and length with different Electric traction Diesel Traction speed, and then calculate the increment of aerodynamic Design running speed of passen- Single- Double- Single- Double- drag. ger train (km/h) The paper herein deals with a calculation method of track track track track additional aerodynamic drag in single-tracked tunnel. İ120 37 31 When a train goes through a single-tracked tunnel, İ160 42 76 42 76 there exists directional airflow in tunnel. Then we can deduce average aerodynamic drag formula theoretically. 200 50 80 50 80 Air cannot spread due to being restrained by tunnel 250 58 90 58 90 when train is running in tunnel, leading the piston phe- 350 70 100 70 100 nomenon, i.e. the difference between head positive pres- Without considering requirements of sure and tail negative pressure, which produces the re- Remarks sistance to the train. Meanwhile, the turbulent flow in double-decked container trains tunnel produces friction between the air and the surface Unit aerodynamic drag in the tunnel is of the train and the tunnel, which also generates the re- sistance to the train. Therefore, when the train is running hFt wt , in the tunnel, aerodynamic drag acting on the train is far ()PGg more than that in the open. The aerodynamic drag in- where h is unit difference of air pressure, in N/m2: crement is called additional aerodynamic drag in the J 2 tunnel. hK (), vv0 In the calculation of aerodynamic drag increment in 2 the tunnel, a series of parameters need to be determined where K is the effect coefficient of piston pressure: first, such as the frictional resistance coefficient of the NL 86u 104 L train surface, frictional resistance coefficient of tunnel K tr tr , (1FF / )22 (1 FF / ) surface, the pressure drag coefficient of the train head tr t tr t 14 Sirong YI et al. / Reasonable compensation coefficient of maximum gradient in long railway tunnels where Ltr is length of train, in m, and Ftr is area of cross- than 160 km/h, it is taken as 22.5 m for single-track tun- DOI:section 10.1007/BF03325733 of train, taken as 12.6 m2; Ȗ is the density of air, nel, and 31.55 m for a double-track tunnel. When design 3 taken as 1.2 kg/m ; v is speed of train, in m/s; v0 is wind speed is in the range of 160 to 200 km/h, it is taken as speed in piston, in m/s: 34.5 m for a double-track tunnel. When design speed is v in range of 200 to 250 km/h, it is 28.0 m for a single- v0 , 1/ ] K track tunnel and 35.0 m for a double-track tunnel. When t design speed is in the range of 250 to 350 km/h, it is where ȗt is total resistance coefficient of tunnel: 32.0 m for a single-track tunnel and 37.5 m for a double- LL track tunnel.
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