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1 45 * Howe. Howe.5 Howe Theoretical study on the compression wave produced by a train entering tunnel -Application of acoustic theory to the case of high blockage ratio problem- Tokuzo IYACHI, Environmental Engineering Division, Railway Technical Research Institute Satoru Ozawa, Professor emeritus, Tokyo University of Technology Takakage Arai, Department of Aerospace Engineering, Osaka Prefecture University (Received 3 September, ; in revised form 3 January, ) When a high-speed train enters a tunnel, a compression wave is generated in the tunnel. The compression wave causes several problems, i.e., ear discomfort, the micro-pressure wave, etc. Hence, it is a very important problem to investigate and predict the compression wave in the tunnel for high-speed railways. Howe has made an unsteady analytical investigation, using acoustic theory, of the compression wave produced by a high-speed train entering a tunnel in the case of low blockage ratio problem ( <.) such as Japanese Shinkansen (Howes theory). In this study, we made an analytical investigation to extend the Howes theory so as to predict the waveform of the compression wave in the case of higher blockage ratio problem ( ~.5) by taking account of the higher order source terms. The results of this study are found to be in excellent agreement with those of the previous steady analytical investigation and the field measurements in real tunnel. (KEY WORDS): High-speed train, Compression wave, Train entering tunnel, icro-pressure wave, Shinkansen, Acoustic theory * miyachi@rtri.or.jp
2 46 ), ) ) ) 3), 4) ), 5) 969 6) 7) 6) 7) 7) Sugimoto 8), 9) monopole Howe )3). Howe 3 CFD Howe 4)6).5 6), 7) Howe Howe Howe. (a) R =. a b a / b 3 (a) (b) R =.48 7) (b)
3 47 A B A B p (kpa) U = 69 km/h =. =. kg/m 3 R =. a/b = 3 p (kpa).5 U = 79 km/h =.64 =. kg/m 3 R =.48 5 ms s Experiment Hara Eq.(.) Howe Eq.(.) with fins without fins Hara Eq.(.) Howe Eq.(.) (a) (b) (a) odel experiment by mirror image method: circular tunnel model with cross-sectional area A = 5 mm, revolution of ellipsoid nose train model of a / b = 3 (b) Field test: horseshoe shaped single tracked tunnel with cross-sectional area A = 8.4 m, snub nose conventional train A B 6), 3) A A B B 6) p G p G R U R (.) UR =U/c c (.) (.) U ~ 8 m/sr ~. p ~ kpa U ~ 3 m/sr ~.5 p ~ kpa kpa Howe Howe ) p H UR 3 UR R 3R ph U (.) Howe R (.) Howe ) p H,A UR UR R R ph, A U (.3) (.)(.3)Sugimoto 8) Howe ) monopole Sugimoto (a) Howe
4 Conventional train on single track uu u R.5 Howe pg ph pg. Shinkansen (b) Howe Howe pg ph pg R > Howe R..3 Howe. 3 3U p A A 3 3u u (a) (d) (a) (b),, Compression wave p, c p, u U p = p, = u Train Region Region Region 3
5 49 (c) (d) c = p / (a)(b) (c)(d).3 3 p p p cu (.4) 3 p p p p p (.5) (.6) A U u A A U u p p U u U u (.7) (d) = (.5) p p X X, X p p (.4) X (.8) X (.9) (.6) X( ) (.) X = R = (A / A ) = u / c = u / c (.7) O[ ]O[ ] X (.) (.)(.) X X A p px U p A (.) (.3) (.3).3 (.) 6) (.)(.3) (.) 6) 4 6) B (a) (b) Compression wave p, c s p, u U u p = p, Train Region Region Region 4
6 5 (c) (d) X p p (c) (a) s s Ac A c u (.4) (.5) p c p c u s s p p c s cs u (.6) (b)(c) (.5)(.7)(.4)(.6) (.5)(.7) 8), 9) s c X s c u X (.7) (.8) p c s p c (.9) (.7)X << 3 X X O X (.) 3 p p X 3 c s p 3 OX cs u p (.) 8), 9) (.) X (.7)(.9) c s X OX (.) (.9) (.) X (b) 4 O[X 3 ] 3 O X (.3) (.6)(.)(.3) X OX (.4) O[X ](.) (.4) (.7) (.)(.3)(.4) X X X OX (.5) X X X G R p px U p R G (.6) (.7) (.).4 Howe (.3) (.) O[ ] (.)
7 5 (.)(.5) O[ ] O[ ] (.3)(.)Howe (.) 5 R =. 3 Howe R =.5 R (.4) R R O[ ] X ~ O[ ]O[X ] ~ O[ 4 ] O[X ] O[ 3 ](.7) pg CpG, O R U (.8) Howe (.7) R R 3R,,3 i 3i CpG, OR i (.9) (.3) R C pa, pa U R R i 3i OR i,,3 (.3) (.9)(.3) monopole Sugimoto(.3) monopole (.9) X X.. R=. Hara Eq.(.) Linear Eq.(.3) Howe Eq.(.)...3. R=.5. 5 Howe (.) (.3) Howe (.3)Howe ) R Howe 3 Howe 3. Howe )3) ))3) R..5 Howe ) Howe 3) Howe
8 5 Howe ) D D BH Dt c Dt 6 Howe 3) 3) 6 Howe Howe Howe 7 O t = t H t uhu BH H u (3.), DDt tu B dp u pu f (x +Ut, x, x 3 ) = (3.) H H ( f ) ( f < ) H H ( f ) U = (U,, ) H f t H f U H f U (3.) x H f f s n uuex n H u H U (3.3) x ns 7 7 N 4 Compression wave x x Reference p, c Point U Train O x 3 Region Region N Region 7 Howe
9 53 4 () O[X ] () (3.) B (3) N u ( u x,, ) u (u,, ) (4) (3.)(3.3) c ph t H H H U ux U B t x x x x x H rb H rr r u (3.4) r x x (3.4) 3 O[X ] () (3.) (3.3)(3.) 3 N 3 N O[RX] (3.4) 4 5 ) (3.4) (.) (3.4) x H A T U U xutxx3 t x t x (3.5) A T (x)x L A T (L) = A (3.4) H uu x x x A uu x Ut x x T x 3 x x (3.6) (3.4) 3 H (3.) 3BHB Howe 7 B ) p c u c. u p ux U p c U uc (3.7) u c O[X ](3.7) O[X ]p c u c (.4) B N BN p ux p c uxu (3.8) c (3.8) BN pc t uxu (3.9)
10 54 [t]= t + (x ) / c (3.6)(3.9)(3.4) 3 H H uu x B x x x x A T pc t xutxx3 x x (3.) Howe (3.5) monopole (3.) dipole monopole p m dipole p dn p m p dn Howe ) (3.)( ) p c p m Howe p m p dn UR pm (3.) R pdn pc (3.) p c (3.4) u u u x (3.4) 4 r A H rr r rb r xut B xut r r r r Ut x s t (3.3) O[X ] s (t ), 7 B 8 s u t L p u B p u u, Ut L x ut (3.4) (3.4) 5 u u u u (3.5) 8 u u r rer, x st (3.6) r e r ( x, r, ) r (3.4) 5 H u A U 8 u r u r r r r, x st A (3.7) (3.4) 4 5 (3.4) 4 p db 5 p p db p R pdb u (3.8) p u (3.9) (a.9)(a.) s(t)
11 55 p db p p NL p NL u pnl pdb p (3.) Howe ) (3.) u RU (.4) u (3.)p NL U p p (3.) NL (3.4) 5 pc pm pdn pnl (3.) (3.)(3.)(3.) p c pc U 3 (3.3) (3.3) p c O R U (3.4) (3.3) (.8) O[ p] (3.) p NL U p c c (3.5) (3.)p c p NL = (3.)(3.)(3.) p c (.3) (3.4) BH Howe U R pm t W t m R pdn t pc t Wm t L r * * A U t Wm t Y Y, dy Y Y r (3.6) (3.7) (3.8) A * A Y = y / r = / r W m = p c ([t]) p m ([t]) + p dn ([t]) p c p c () p A (.3)Howe p c p G (.) (3.5)(3.6) (3.7) p NL monopole dipole U pnl t Wm t pc t W t m (3.6)(3.7)(3.9) (3.9) pc t pm t pdn t pnl t (3.3) p c (.)p G (.3)p A t Wm t Wm pc t p pg p p A A G (3.3) (3.3) W m ([]) = (3.3) p c = p c ([]) = p G Howe ) (.) c H m p t p W t (3.33)
12 56 p (kpa) p/t (kpa/s) p/t (Pa/s) s.5 s U = 79 km/h =.64 =. kg/m 3 R =.48 Field test: Snub nose train with fins Eq.(3.3) Howe: Eq.(3.33) 9 Experiment Eq.(3.3) Howe: Eq.(3.33) U = 69 km/h =. =.4 kg/m 3 R =. a/b = 3 (3.3)(3.33) 4 Howe (.3) (.) Howe Howe (3.)(3.3) (3.7) ms t (b)(3.3) (3.33) 9 (3.3)Howe (3.33) =.U = 69 km/hr =. (3.3)(3.33) a / b = 3 (3.3)
13 57 Howe ) O[R 3 ] Howe ) p dn monopole p dn p dn Howe (3.3) 9 (3.3) (3.3) c G m (4.) p t p W t 5 Howe () Howe dipole (3.) (.3) Howe () Howe (3.3)(3.7) (.8) Howe (3.4) (3) Howe (3.3) (3.)Howe ) c Gxy,, t A x y x y * * * * Ht Ht c c (a.) * * ) = * / r (a.)monopole (3.5) x << r p t m A T U y U y y3 G t dd x * 3 xy,, y (a.) y, U R pm pm (a.3) (3.) Gc t * A y t y (a.4) (a.)(3.6) dipole (3.) pd t y pc y y y c 3 y 3 G d y (a.5) (a.5)(a.3)(3.)(a.4) y * G y A y c t y (a.6) (a.5) y p c
14 58 (3.7) p db y y3 * t t y, c G G xy,, t A * y, t t (3.3) H G pdb x, t B ddyd p db (3.4) * ru, A r Ru pdb y r dy (3.7) p u G p x, t r r ddyd * ru, A r u p y r dy (3.8)(3.) G n G n y r, n,,3 (a.7) (a.8) (a.9) (a.) (a.) (a.) (a.3) () () t y << r (a.) t (a.3)() 3 4 BH x c UA x x x p A x x x (a.4) 3 3 (a.4) 3 4 A A B AB AU A pc (a.5) B p c B c Ap AU A p (a.6) p c (.3) B p c B u / Apc AA u AU Apc (a.7) (.4) u p c (3.3) 3.3 X 6) X X X X X X X c (a.8) (a.8) X (.6) (a.8)x Howe Pope 9), ) 7) (.8)Howe (3.4) BH x ) :,,,,
15 59 (977). ) :,, (979). 3) :,, (998). 4),,,, :, B, 6 (996) ) :,, 4 (995) ) :,, 6 (96) ) :,, 3 (983). 8) N. Sugimoto: traveling of a high-speed train, Theoretical and Computational Acoustics, (994) ) N. Sugimoto & T. Ogawa: Acoustic analysis of the pressure field in a tunnel, generated by entry of a train, Proceedings of The Royal Society of London, A 454 (998) 83-. ). S. Howe: The compression wave produced by a high-speed train entering a tunnel, Proceedings of The Royal Society of London, A 454 (998) ). S. Howe: ach number dependence of the compression wave generated by a high-speed train entering a tunnel, Journal of Sound and Vibration, (998) ). S. Howe,. Iida, T. Fukuda & T. aeda: Theoretical and experimental investigation of the compression wave generated by a train entering a tunnel with a flared portal, Journal of Fluid echanics, 45 () -3. 3). S. Howe,. Iida, T. aeda & Y. Sakuma: Rapid calculation of the compression wave generated by a train entering a tunnel with a vented hood, Journal of Sound and Vibration, 97 (6) ),, :,, (7) ) K. Kikuchi,. Iida & T. Fukuda: Optimization of Train Nose Shape for Reducing icro-pressure Wave Radiated from Tunnel Exit, 4th International eeting on Low Frequency and Vibration and its Control, () CD-RO. 6),, :,, (8) CD-RO. 7),, :, C, 76 () ), :,, 96. 9) :,, (994). ) W. A. Woods & C. W. Pope: Secondary aerodynamic effects in rail tunnels during vehicle entry, nd BHRA Symposium on the Aerodynamics and Ventilation of Vehicle Tunnels, C5 (976) 7-79.
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