Numerical simulation on wind pressure transients in high speed train tunnels

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1 Compters in ailways XI 905 Nmerical simlation on win pressre transients in high spee train tnnels S.-W. Nam Department of High Spee Train, Korea ailroa esearch Institte, Korea Abstract When a train passes throgh a tnnel with high spee, pressre waves are generate e to the entry of the front an the rear of the train respectively. These pressre waves are alternately propagate an reflecte at the exit an entrance of the tnnel. Severe pressre transients case the repeate fatige loa to the car-boy an tnnel wall, ear-iscomfort to passengers, an micro pressre wave to the srronings of the tnnel exit. To clarify qantitative pressre change in the tnnel is very important for the optimal esign of the tnnel size. Partial ifferential eqations also can be converte into orinary ifferential eqations by sing the metho of characteristics. In this sty, we have evelope a simlation program to calclate pressre transients in a railroa tnnel. The metho of characteristics base on a fixe mesh system is se to solve the governing eqations. By sing this program, we have preicte pressre transients in KTX (Korea Train express)-tnnel an compare with experimental reslts that are obtaine in Unj tnnel with KTX high spee trains. The reslts of calclation coincie with the ones of the Unj tnnel tests, an the pressre transient mechanism was mae clear. To analyze the effects of train spee an blockage ratio, we have concte parametric simlations. The reslts show that pressre rise in a tnnel is proportional to the sqare of train spee an to the blockage of train/tnnel cross sectional area. Keywors: win pressre, high spee train, tnnel flow, pressre wave. Introction When a train enters an passes throgh a tnnel with high spee, a compression wave is generate e to the entry of the train hea an an expansion wave is ISSN (on-line) WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press oi:0.495/c4076

2 906 Compters in ailways XI generate e to the entry of the train tail. These pressre waves propagate along the tnnel an reflect in trn at the exit an entrance of the tnnel. So, a complex wave phenomenon appears in the railway tnnel. Severe pressre transients case the repeate fatige loa on the car boy an tnnel wall, ear-iscomfort to passengers, an micro pressre wave to the environment []. Flow in the long tnnel can be assme as a one-imensional internal pipe flow ner the assmption that variables in a constant cross section of the tnnel are the same. Becase pressre increase in the tnnel is proportional to the sqare of train spee, it is very important to esign the optimal tnnel esign, rag rection of train, worker s safety in tnnel, an stress increase of car boy. In orer to nerstan complex pressre transient phenomena in a tnnel, real train test is the most effective metho. Bt, to o real train experiment is a time an manpower consming approach. So, many researchers choose the nmerical simlation to replace that. W [] an Szki [] se -imensional moel to clarify pressre transient in a tnnel an Kwon et al. [] se an axisymmetric one. Bt, these methos nee lots of comptational mesh an long compting time in the case of a long tnnel moel. Figre : Pressre transient in a tnnel. Yamamoto [4] set a one-imensional moel ner the assmption that flows in the same cross section of a tnnel are almost constant. After that, Maea improve the methos an ary an Dayman [5] an Kim [6] applie to the analysis of pressre transient in a tnnel. Almost all the preceent researches se the variable mesh system to calclate the characteristics crves an the position of train. In this sty, fixe mesh system is aopte. Simlation reslts with characteristics metho are compare with that of real train experiment an showe goo coincience qantitatively an qalitatively. Nmerical calclation an etails One-imensional governing eqations can be written as follows ner the assmption that variables in constant cross section of a tnnel are the same. t x p f x () WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

Compters in ailways XI 907 p p a ( ) ( ) () x t x These partial ifferential eqations also converte to orinary ifferential ones following to characteristics crves of C+ an C- [7].

3 Compters in ailways XI 907 p p a ( ) ( ) () x t x These partial ifferential eqations also converte to orinary ifferential ones following to characteristics crves of C+ an C- [7]. ( p a) ( ) af () t ( p a) ( ) af (4) t Friction force an energy issipation can be escribe as following the position of the train (shown in Figs an ). Figre : Calclation omain. Figre : Distance-time iagram. Domain : f (5) (6) WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

4 Domain : ) ( f (7) (8) Domain : ) ( ) ( f (9) (0) Accoring to the railroa track an train type, a proper friction coefficient can be aopte an bonary conitions at a tnnel inlet an otlet are as follows: Tnnel inlet: p : in case of 0 () 0 p : in case of 0 Tnnel otlet: p : in case of 0 () 0 p : in case of 0 In this sty, fixe mesh system is se to calclate velocity an pressre whereas preceing sties se variable mesh one. In the fixe mesh system, we on t nee to calclate intersection point of two characteristics crves every time. Figre 4: Fixe rectanglar mesh. Between point P an A on the crve C+, point P an B on the crve C-, iemann invariant can be obtaine. Pressre an velocity of point P on time step t+ t also are calclate by sing vales of gri point i, i+, an i- on time step t. 908 Compters in ailways XI ISSN (on-line) WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press

5 Compters in ailways XI 909 Depenent variables at point A an B are calclate by interpolating with vales of mesh i, i-, an i+. Then, Pressre an velocity of point P on the characteristics crves of C+ an C- are obtaine as follows [8]; where Q Q U A B P a () QA QB PP (4) QA [( ) af ] At PA QB [( ) af ] B t PB au A au B Bonary conitions at the train hea an tail are also written by simltaneos eqations. Figre 5: Bonary conition of train hea. In Fig. 5, when the train hea is locate in the position between P an Q, simltaneos eqations can be applie. ( P au ) P ( P au ) A 0 (5) ( P au ) Q ( P au ) B 0 (6) ( )( U P ) U Q (7) PP ( U P ) PQ ( UQ ) (8) So, pressre an velocity for each point, P an Q, are obtaine simltaneosly. An, calclation time step t is etermine by gri size an son spee as follows. x t (9) Ca WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

6 90 Compters in ailways XI Accoring to the Corant-Frierichs-Lewy conition, constant C set as. Overall procere of calclation is as in the following. At first, ivie the tnnel into eqally-space meshes an assign initial conitions of pressre an velocity as 0 at time step t=0. Calclate pressre an velocity of internal meshes of the tnnel by sing Eqs. () an (4) at time step t+t. At the same time, calclate the position of train hea an tail. An then, apply bonary conitions of Eqs. (5) (8) to connection points of train hea an tail. enew inlet an otlet conition of the tnnel of Eqs. () an (). epeat these proceres ntil the train goes throgh the tnnel exit. eslts In orer to compare simlation reslts with experimental ones, the real train experiment sing Korean high spee train, KTX, has been concte in Kyngb line. Comparison target is Unj tnnel that measres 400m in length an KTX train enters the tnnel with travelling spees of 65km/h. Sie pressre variation on the hea of train going throgh Unj tnnel is shown in Fig. 7. There is atmospheric pressre ifference of 80 Pa between the tnnel inlet an otlet becase the tnnel slopes gently own by 8. When the train enters an passes throgh the tnnel with high spee, a compression wave is generate e to the entry of the train hea an an expansion wave is generate e to the entry of the train tail. These pressre waves propagate along the tnnel an reflect in trn at the exit an entrance of the tnnel. So, complex phenomenon of pressre wave appears in the railway tnnel. When the train meets with an expansion wave as point, a pressre ecrease occrs whereas pressre increases with compression wave as point. Comparison between simlation an experiment of pressre transients is shown in Fig. 7. Figre 6: X-t iagram. WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

7 Compters in ailways XI Unj tnnel : 400 m Train Spee : 65 km/h Simlation Experiment Pressre (Pa) A(058) 5 6 B(0645) Time (sec) Figre 7: Comparison between simlation an experiment. In the figre, the simlation reslt is represente by a re line an experimental one is a ble line. The reslts of simlation correspon with that of experiment qalitatively an qantitatively. In the latter half of tnnel, there is some iscrepancy in pressre changing pattern. It is consiere that pressre waves propagate with the spee of son in simlation bt these waves are istrbe by varios obstacles in real tnnel, for example, srface roghness of tnnel, by-pass tnnel for fire an ventilation, maintenance facilities, sleepers, ballast, an electric power catenary eqipment etc. After the train enters the tnnel, pressre increases ntil train hea meets with expansion wave at point. The range of pressre increase of simlation an experiment are 650 Pa an 700 Pa respectively. An the range between point an point are 6 Pa an 06 Pa =0.07 =0.00 =0.0 Pressre (Pa) Time (sec) Figre 8: Effects of friction coefficient. Figre 8 shows the effects of friction coefficient of the train srface. It is consiere that small vale of friction coefficient means a streamline type of train shape. From the figre, we know that small friction coefficient for train WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

8 9 Compters in ailways XI srface reslts in the small pressre increase when train enter tnnel. So esign for streamline shape is an effective metho to rece pressre increase in a tnnel km/h 00 km/h 50 km/h Pressre (Pa) Time (sec) Figre 9: Effects of train velocity. Figre 9 represents the effects of velocity of train entering tnnel. In case of train spee of 50 km/h, 00 km/h, an 50 km/h, pressre increase are 77 Pa, 0 Pa, an 55 Pa respectively. So pressre increase at tnnel inlet part is approximately proportional to the sqare of train velocity. Figre 0 compare the effects of tnnel cross sectional area for pressre variation. Three cases for tnnel area of 07 m, 00 m, an 90 m have been chosen to compare the effects to pressre variation m 00 m 90 m Pressre (Pa) Time (sec) Figre 0: Effects of tnnel cross section area. It is clear that the range of pressre increases in case of 07 m is smaller than that of small tnnels. To make a tnnel big it is effective to rece pressre increase in the tnnel, bt the cost to constrct the tnnel reversely increases. WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

9 Compters in ailways XI 9 4 Conclsions In this sty, we have evelope a simlation program to calclate internal pressre transients in railroa tnnel. Characteristics metho base on fixe mesh system is se to solve one-imensional governing eqations. By sing this program, we have preicte pressre transients in KTX (Korea Train express)-tnnel. Comparisons are also mae with high spee train, KTX, measrements obtaine in Unj tnnel. The reslts of calclation coincie in ones of the Unj tnnel tests, an pressre transient mechanism was mae clear. It is consiere that small vale of friction coefficient means streamline type of train shape. From the reslts, small friction coefficient for train srface reslts in the small pressre increase when train enter tnnel. So esign for streamline shape is effective metho to rece pressre increase in tnnel. To analyze the effects of train spee an blockage ratio, we have concte parametric simlations. Pressre rise in tnnel is proportional to the sqare of train spee an to the blockage of train/tnnel cross sectional area. In the following sty, it is necessary to consier variable train spee in tnnel an the effects of by-pass tnnel for practical moel. Acknowlegement This sty was spporte by research fns from Korea ail Network Athority. eferences [] P.K.H. W. Preiction of Pressre wave generation by high-spee train entering tnnel sing a commercial CFD coe, BH Grop 000 ehicle Tnnels,, pp , 000. [] M. Szki. Aeroynamic Force acting on Train in Tnnel, TI eport, 4(9), pp. 7-4, 000. [] H.B. Kwon, T.Y. Kim, D.H. Lee, M.S. Kim. Nmerical simlation of nsteay compressible flows ince by a high-spee train passing throgh a tnnel, Proc. Inst. Mech. Engrs. Part F: J ail an api Transit., 7, pp. -4, 00. [4] A. Yamamoto. Aeroynamics of Train an Tnnel, TI eport, 0, pp. -70, 98. [5] A.E. ary, B. Dayman. Alleviation of Tnnel Entry Pressre Transients: Theoretical Moelling an Experimental Correlation, r Int. Symp. on the Aeroynamics an entilation of ehicle Tnnels, pp. 6-75, 979. [6] Hey-Dong Kim. Aeroynamic Analysis of a Train nning in a Tnnel()- Aeroynamics of One-Train, J. Korean Society of Mechanical Engineers (B), (8), pp , 997. [7] G. inger. Wave Diagrams for Nonsteay Flow in Dcts, D. an Nostran Co. Inc., New York. pp. 8-9, 955. [8] C.Y. Chow. An Introction to Comptational Fli Mechanics, John Wiley & Sons, Inc. pp , 979. WIT Transactions on The Bilt Environment, ol 5, 04 WIT Press ISSN (on-line)

Mehmet Pakdemirli* Precession of a Planet with the Multiple Scales Lindstedt Poincare Technique (2)

Mehmet Pakdemirli* Precession of a Planet with the Multiple Scales Lindstedt Poincare Technique (2) Z. Natrforsch. 05; aop Mehmet Pakemirli* Precession of a Planet with the Mltiple Scales Linstet Poincare Techniqe DOI 0.55/zna-05-03 Receive May, 05; accepte Jly 5, 05 Abstract: The recently evelope mltiple