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Fluid Dynamic Problems of High-Speed Trains in Tunnels

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Fluid Dynamic Problems of High-Speed Trains in Tunnels UNIVERSIDAD POLITÉCNICA DE MADRID Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio Fluid Dynamic Problems of High-Speed Trains in Tunnels Juan Manuel Rivero Fernández Ingeniero Mecánico Madrid, 2018 Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio Departamento de Mecánica de Fluidos y Propulsión Aeroespacial Fluid Dynamic Problems of High-Speed Trains in Tunnels Autor Juan Manuel Rivero Fernández Director de la Tesis Manuel Rodríguez Fernández Madrid, 2018 Tribunal nombrado por el Sr. Rector Magfco. de la Universidad Politécnica de Madrid, el día...............de.............................de 20.... Presidente: Vocal: Vocal: Vocal: Secretario: Suplente: Suplente: Realizado el acto de defensa y lectura de la Tesis el día..........de........................de 20.... en la E.T.S.I. /Facultad.................................................... Calificación .................................................. EL PRESIDENTE LOS VOCALES EL SECRETARIO Contents Agradecimientos v Resumen vii Abstract ix 1 Introduction 1 1.1 Problem description . 1 1.2 Bibliographical research . 5 1.3 Publications . 13 2 Conservation equations 15 2.1 Mass conservation . 15 2.2 Momentum conservation . 16 2.3 Energy conservation . 17 2.3.1 Energy conservation principle . 17 2.3.2 State equations . 18 2.4 Navier-Poisson and Fourier Laws . 20 2.4.1 Kinematic coefficients . 22 3 Flow in conducts 25 3.1 Governing equations for a tube . 28 3.1.1 Continuity equation . 28 3.1.2 Momentum conservation . 29 3.1.3 Energy equation . 32 3.2 Friction coefficient and heat flux . 35 3.3 Governing equations for a cylinder in a tube . 37 3.3.1 Continuity equation . 37 3.3.2 Momentum equation . 38 3.3.3 Energy equation . 40 3.3.4 Change to a system of reference fixed to the tunnel . 42 4 Ideal Fluids: Euler equations 45 4.1 Movements at high Reynolds . 45 4.2 Initial and boundary conditions . 46 i ii CONTENTS 4.3 Continuity and existence of the solution . 47 4.4 The speed of sound . 47 4.5 Isentropic and homentropic movements . 47 4.6 Stagnation magnitudes . 49 4.7 Unidimensional flow . 50 4.8 Lineal waves . 51 4.9 Non lineal waves . 53 4.9.1 Riemann variables . 54 4.9.2 Simple waves . 55 4.9.3 Examples . 57 5 Kirchhoff's integral formula 63 5.1 Governing equations . 63 5.2 Energy equation for the sonic field . 66 5.3 Plane waves . 68 5.4 Sound emission . 70 5.4.1 Spherical waves. Acoustic monopole . 70 5.4.2 Continuous distribution of monopoles . 72 5.4.3 Superficial sources distribution . 75 5.4.4 Acoustic dipoles . 76 5.4.5 Kirchhoff's integral formula . 78 6 Flow equations around a train in a tunnel 81 6.1 Health and comfort limits . 81 6.2 Governing equations in the tunnel . 84 6.3 Order of magnitude of (∆p)c, uc and (∆T )c . 84 6.4 Simplification of equations far from the train . 89 6.4.1 Solution for times of order t0 ∼ LT r=U . 91 6.4.2 Solution for times for which the friction and heat conduction are important . 92 6.4.3 Times for which the pressure wave is damped . 92 6.4.4 Infinitely long tunnel . 94 6.5 Governing equations between train and tunnel . 94 6.5.1 Equations along the characteristics in the gap between train and tunnel . 96 6.5.2 Flow around the nose and tail . 98 6.6 Discretized equations for the numerical model . 105 6.7 Comparison with experimental data . 110 6.8 Comparison with the infinitely long tunnel solution . 116 6.9 Temperature distribution inside the tunnel . 117 6.10 A chimney in a long tunnel . 119 CONTENTS iii 7 Prediction of the Sonic Boom 127 7.1 One-dimensional flow equations . 127 7.2 Boundary condition at the entry section . 130 7.3 Approximation of the initial pressure profile . 130 7.4 Isentropic algebraic solution . 132 7.5 The numerical model . 135 7.6 Validation of the model . 138 7.7 Parametric analysis . 143 7.8 Micro-pressure wave emission . 145 8 Wall temperature in long tunnels 155 8.1 Period with the train inside the tunnel . 155 8.2 The heat equation on the rock . 159 8.3 Period with the train outside the tunnel . 160 8.4 Initial and boundary conditions . 162 8.5 Numerical scheme . 163 8.6 Comparison with the model from chapter 6 . 164 8.7 Results of the temperature rise . 165 8.8 A pseudo-similarity solution . 166 9 Conclusions 171 Bibliography 180 A Numerical scheme for the chimney 181 A.1 Governing equations . 181 A.2 Coupling with the tunnel . 183 B Analytic solution for the chimney 185 B.1 Continuity . 185 B.2 Momentum . 185 B.3 Energy . 188 B.3.1 Adiabatic case . 189 B.3.2 Isotherm case . 189 B.3.3 Wall temperature with a lineal distribution . 190 B.4 Quasi-steady assumption . 190 B.5 Comparison with the numerical solution . 191 2 2 C The value of τ(@θR=@τ)=(@ θR=@ζ ) when τ 1 197 iv CONTENTS Agradecimientos Esta tesis es el fruto de trabajo de m´asde tres a~nosde investigaci´on,esfuerzo, frustra- ciones y victorias; decir que Manuel Rodr´ıguez, mi tutor y mentor, es el mayor co-autor de ella es quedarse corto. Sin el, nada de esto se habr´ıalogrado. No solo me gui´oa trav´es del intrincado laberinto que puede ser realizar un doctorado, sino que adem´asme ense~n´o a utilizar herramientas, como los ordenes de magnitud, que ser´animprescindibles para el resto de mi vida profesional. Su tenacidad, sabidur´ıay paciencia estar´ansiempre en mi coraz´on. Quiero agradecer tambi´ena Benigno L´azaropor toda la ayuda con la parte num´ericade la investigaci´on;a Ezequiel Gonz´alez,que adem´asde haberme apoyado en incontables ocasiones, es co-autor de los art´ıculos que fueron resultado de estos a~nosde investigaci´on; a Jos´eManuel Vega de Prada por sus consejos para el ´ultimocap´ıtulode la tesis; y a Rafael Rebolo, por su aportaci´oninvaluable con el tema de temperatura en t´uneles. A Mukh, por echarme la mano con la gram´aticadel ingl´es,y el apoyo moral en tantos jams. A Susie Q, por todo el impulso, motivaci´ony cari~noque me di´opara volar en la recta final. A mis padres, mi hermana y mis hermanos, que siempre me han dado su amor incondi- cional. A Ram´on,por el cari~noy pasi´ona esta vocaci´on. A todos mis amigos que me dieron ´animo,fuera estando cerca o lejos. Y por ´ultimo, pero no por ello menos importante, al CONACYT que crey´oen mi, y que me di´olos recursos para poder cumplir este sue~no. Nada de esto hubiera sido posible sin ellos. v vi AGRADECIMIENTOS Resumen Es bien conocido que Espa~naes uno de los pa´ısescon m´askilometros de v´ıade alta ve- locidad, de los cuales la mayor´ıase encuentran a la mayor altitud en Europa, atravesando zonas monta~nosas a trav´esde un gran n´umerode t´uneles.El movimiento de trenes de alta velocidad en t´unelesgenera una multitud de fen´omenosfluidodin´amicosque generalmente se encuentran asociados a ondas de presi´onque viajan por su interior; dada la magnitud de las dimensiones de los t´uneles,es necesario predecir la din´amicade dichas ondas con herramientas de c´alculolo m´assimples posible, pero que describan adecuadamente el pro- ceso f´ısico. En el presente trabajo se analizan los detalles del flujo en las distintas regiones del movimiento, reteniendo en cada una de ellas los efectos m´asrelevantes, para as´ıgenerar un programa de c´alculoque permite determinar el complejo flujo en el interior del t´unel de forma r´apiday eficiente. De este modo se puede determinar, en las etapas prelim- inares del proyecto de dise~node un t´unel, los denominados l´ımitesde salud y confort, que se deben cumplir de forma obligatoria, en especial el de salud. Se podr´ıapensar que utilizando programas comerciales de Mec´anicade Fluidos Computacional (CFD) se ob- tendr´ıanresultados de forma sencilla, pero nada m´aslejos de la realidad ya que para tener una resoluci´onadecuada de las ondas que viajan por todo el t´unel,el n´umerode nodos requerido es inmenso y los tiempos de c´alculoprohibitivos. Los m´etodos CFD se pueden utilizar para generar la onda inicial durante el par de d´ecimasde segundo que tarda en entrar la cabeza del tren en el t´unel,y para ello es necesario mallar adecuadamente los primeros 100 ´o200 primeros metros del t´unel;sin embargo, la propagaci´ona lo largo de kilometros de t´unel,dada la naturaleza casi unidmensional del flujo, se puede modelar utilizando ecuaciones simplificadas que ahorran tiempo de implementaci´ony c´alculo com- putacional, sin perder la informaci´onf´ısicarelevante. En este trabajo se analiza tambi´enla propagaci´ony distorsi´onde la primera onda gener- ada por la cabeza del tren al entrar en el t´unel,que est´acaracterizada por dos par´ametros b´asicos: el incremento m´aximode presiones inicial y la pendiente m´axima de la dis- tribuci´onde presiones inicial. Esta onda es susceptible de producir una onda de choque en el interior del t´unel,que al reflejarse en la boca opuesta del mismo, genera ondas de micro presi´onen el exterior, dando lugar a un estallido s´onicoque puede afectar a las zonas pobladas en las cercan´ıasdel t´unel.Por medio de un modelo unidimensional, que utiliza el m´etodo de las caracter´ısticas,se determinan los par´ametrosde la onda citados anteriormente, que permiten asegurar que el estallido s´onicono se produzca en un t´unel dado por el que circulen trenes de alta velocidad.
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