Aeroacoustics in high speed trains

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(1)Universidad Politécnica de Madrid. Doctoral dissertation:. AEROACOUSTICS IN HIGH SPEED TRAINS by. Félix Sorribes Palmer. Advisors: Prof. Dr. Ing. Ángel Sanz Andrés Prof. Dr. Ing. Gustavo Alonso Rodrigo. E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, December 2014.

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(3) Resumen Este trabajo se centra en el estudio de problemas aeroacústicos en los trenes de alta velocidad. Se han considerado dos escenarios en los que las ondas de presión generadas son críticos para el confort de los pasajeros. Uno es el debido a las ondas de presión que genera el tren cuando entra y sale de un túnel, que a su vez producen saltos de presión de baja frecuencia en el tren (cuando se cruzan con él) y en los alrededores del túnel cuando alcanzan la salida. Se estudia este fenómeno, y se propone un sistema aeroelástico basado en el galope transversal para disminuir la energía de estas ondas, y se analiza la energía extraíble de las ondas utilizando cuerpos con diferentes secciones transversales [Sorribes-Palmer and Sanz-Andres, 2013]. La influencia de la geometría de los portales en la energía radiada hacia el exterior de túnel es analizada experimentalmente, prestando especial atención a las boquillas porosas. Las ondas de presión en el interior del túnel se han analizado mediante el método de las características. Se han realizado ensayos experimentales para estimar la energía reflejada hacia el interior del túnel al alcanzar las ondas de presión el portal de salida del túnel. Se ha estudiado la formación e interacción entre el portal del túnel y la onda de choque generada en los túneles de gran longitud y pequeña fricción. Se propone un método para describir de forma aproximada el ruido radiado al exterior. Por otro lado se ha estudiado el ruido de media y alta frecuencia de origen aerodinámico. Se ha estudiado la influencia del desprendimiento de la capa límite sobre el tren. Se propone una metodología basada en una sección de tren característica para predecir rápidamente el nivel de presión de sonido dentro y fuera del tren para todo el rango de frecuencias. Se han realizado medidas experimentales en vía de los espectros de presión sobre la superficie del tren, y de la transmisibilidad de las uniones entre estructura y revestimiento. Los resultados experimentales se han utilizado en los modelos vibroacústicos. El método de la sección del tren característica es especialmente útil a altas frecuencias cuando todo el tren se puede modelar mediante el ensamblaje de diferentes secciones características utilizando el análisis estadístico de la energía..

(4) Summary This work is focused on the study of aeroacoustic problems in high speed trains. We have considered two scenarios in which the pressure waves generated are critical for passengers comfort. The first one is due to the pressure waves generated by a train entering in a tunnel. These waves generate pressure gauges inside the train (when they find each other) and outside of the tunnel portals. This phenomenon has been studied, and an aeroelastic system based on transverse galloping to reduce the energy of these waves is proposed. The maximum extractable energy by using bodies with different cross-section shapes is analyzed. The influence of the portals geometry in the energy radiated outwards the tunnel is analyzed experimentally, with particular attention to the porous exits. The pressure waves inside the tunnel have been analyzed using the method of characteristics. Experimental tests to estimate the energy reflected into the tunnel when the pressure waves reach the tunnel portal have been performed. We have studied the generation and interaction between the tunnel portal and a shock wave generated in long tunnels with small friction. A method to describe in an approximated way the pressure radiated outside the tunnel is proposed. In the second scenario, middle and high frequency noise generated aerodynamically has been studied, including the influence of the detachment of the boundary layer around the train. A method based on a train section to quickly predict the sound pressure level inside and outside the train has been proposed. Experimental test have been performed on board to evaluate the pressure power spectra on the surface of the train, and the transmissibility of the junctions between the structure and trim. These experimental results have been used in the vibroacoustic models. The low frequency pressure waves generated with the train during the tunnel crossing has been identified in the pressure spectrum. The train characteristic section method is especially useful at high frequencies, when the whole train can be modeled by assembling different sections using the statistical energy analysis. The sound pressure level inside the train is evaluated inside and outside the tunnel..

(5) Acknowledgments. First of all I would like to acknowledge the director of Instituto Universitario de Microgravedad “Ignacio Da Riva”, Prof. Dr. Ing. José Meseguer, for giving me the opportunity to work in the institute. I have been able to work in different areas and learn a lot from many persons in the institute, specially from my advisors Prof. Dr. Ing. Angel Sanz Andrés and Prof. Dr. Ing. Gustavo Alonso Rodrigo, and i want to thank them their patience to listen and explain every time I needed it. I also want to thank the rest of the people of the institute for their support: Álvaro Cuerva, Oscar López, Santiango Pindado, Sebastian Franchini, Javier Pérez, Isabel Pérez, Alejandro Martínez, Mohsen Ghaemi, Rafael García, Sergio Ávila, Alejandro Gómez, etc.. I want to thank the late Prof. Dr. Ing. Jesús López Díez for all his help on introducing me to the world of vibroacoustics. I am really grateful to Universidad Politécnica de Madrid for the scholarship to spend a three months visit at TU Berlin, where they let me use their facilities to perform experimental test and also helped me to understand vibroacoustic modeling, this experience was highly useful to focus my work and to push forward this dissertation. I want to thank my friends for cheering my up during the tough moments and for sharing their time with me: Marcos, Diego, Laura, Joseba, Eduardo, Pedro, etc. I render thanks to Dani for reading everything I gave him. Lastly, I would like to thank my family, for their support and encouragement, because having them by my side made everything look possible. And most of all for my loving girlfriend Julija for her patience, unconditional love and faithful support. A life full of possibilities is open to us now, and I am willing to explore it with you “ljubezen”, rtm..

(6) Contents. Contents. i. List of Figures. iii. List of Tables. ix. 1 Introduction 1.1 Noise sources in high speed trains . . . . . . . . . . . . . . . . . . . . . 1.2 Objectives and content structure . . . . . . . . . . . . . . . . . . . . . .. 1 1 9. 2 Pressure waves in high speed railway tunnels 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Mathematical model for prediction of pressure waves inside a tunnel . . . 2.2.1 Condition for the existence of a plane wave . . . . . . . . . . . . 2.2.2 Propagation of the signature . . . . . . . . . . . . . . . . . . . . 2.3 Hydrostatic pressure influence on high speed railway tunnels cross-section sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Non-linear propagation and pressure wave steepening inside a tunnel . . 2.5 Pressure wave interaction at the tunnel exit . . . . . . . . . . . . . . . . . 2.6 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.1 Reflected wave at the horns . . . . . . . . . . . . . . . . . . . . . 2.7.2 Reflected and transmitted wave at airshafts . . . . . . . . . . . . 2.7.3 Reflected and transmitted wave at a perforated section . . . . . . . 2.7.4 Reflected wave at perforated exits . . . . . . . . . . . . . . . . . 2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 11 15 16 17. 3 Energy extraction from aerodynamic instabilities 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Extracted power in a general case . . . . . . . . . . . . . . . . 3.2.2 Comparison between numerical integration method and polynomial expansion . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Influence of the number of discretization points . . . . . . . . . i. 22 25 29 31 42 42 43 44 45 49. 51 . 51 . 53 . 56 . 60 . 60.

(7) ii. CONTENTS. 3.2.4. 3.3 3.4. 3.5. Comparison of the numerical integration method with the polynomial expansion at a point different from the origin. . . . . . . . . Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Biconvex airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 D-shape body . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Rhomboidal cross-section bodies . . . . . . . . . . . . . . . . . . 3.4.4 Triangle cross-section bodies . . . . . . . . . . . . . . . . . . . . 3.4.5 Square cross-section bodies . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Interior noise prediction in high speed trains 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . 4.2 Numerical analysis . . . . . . . . . . . . . . . . . 4.2.1 Basic acoustic concepts and definitions . . 4.2.2 Methodology . . . . . . . . . . . . . . . . 4.2.3 Structural and fluid models . . . . . . . . . 4.2.4 Loads . . . . . . . . . . . . . . . . . . . . 4.2.4.1 Structure-borne . . . . . . . . . . 4.2.4.2 Airborne . . . . . . . . . . . . . 4.3 Experimental set-up . . . . . . . . . . . . . . . . 4.4 Tests definition . . . . . . . . . . . . . . . . . . . 4.4.1 Aerodynamic noise characterization . . . . 4.4.1.1 SPL in open field . . . . . . . . . 4.4.1.2 SPL inside a tunnel . . . . . . . . 4.4.2 Point junction characterization . . . . . . . 4.5 Interior noise prediction . . . . . . . . . . . . . . . 4.5.1 Flow detachment influence on interior noise 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. 62 65 67 67 70 72 75 76 80 83 83 85 85 93 93 99 99 101 102 104 104 104 105 106 107 108 108. 5 Conclusions and future work 111 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Bibliography. 115. A Appendix A.1 Wave separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Slowly varying cross section ducts . . . . . . . . . . . . . . . . . . . . . A.3 Experimental set-up calibration . . . . . . . . . . . . . . . . . . . . . . . A.3.1 Influence of microphone insertion . . . . . . . . . . . . . . . . . A.3.2 Influence of leakage on microphone holes . . . . . . . . . . . . . A.3.3 Influence of relative humidity . . . . . . . . . . . . . . . . . . . . A.3.4 Influence of pipe junctions . . . . . . . . . . . . . . . . . . . . . A.3.5 Validation of the experimental set-up with analytic expression for the reflection coefficient . . . . . . . . . . . . . . . . . . . . . .. 125 125 128 131 131 131 131 132 133.

(8) List of Figures. 1.1.1 Variation of the sound power levels Lw with train speed Utr of different sound sources (after Lauterbach et al. [2012]). . . . . . . . . . . . . . . 1.1.2 Main sources of interior noise in a train and their transmission paths into the vehicle (after Thompson [2009]). . . . . . . . . . . . . . . . . . . . 2.1.1 Train reference signature defined by the standard EN14067-5:2006:E [2006]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Pressure variation in the tunnel as a function of time, validation of the TWS implementation, M = 0.24 and φ = 0.135. Pressure evolution in the tunnel at 550 m from the tunnel entrance. Experimental results from William-Louis [1999]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Pressure variation at the train as a function of time, validation of the TWS implementation M = 0.24 and φ = 0.135. Pressure evolution in the train at 72 m from the nose. . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Position x of the pressure waves generated by a high speed train inside a tunnel of length Ltun as a function of time t. C, compression: E, expansion wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Tunnel cost (per meter) as a function of the tunnel cross-section area, Atun , for different Rock Mass Ratings (RMR). . . . . . . . . . . . . . . 2.3.2 Pressure inside (red) and outside (blue) the train during pass through a tunnel of 20 km length with 25 ‰ ascendant slope. . . . . . . . . . . . . 2.3.3 Critical cross-section area of tunnels with 25‰ of ascendant slope and length 20, 25 and 30 km. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Variation with time t of pressure P of the wave inside a tunnel. . . . . . 2.5.1 Result for the radiated pressure by the non-linear propagation method. Variation with time of: 1) predicted pressure at the tunnel entrance and exit; 2) pressure gradient at the exit; 3) predicted radiated pressure at r=1 m from the tunnel exit in Pa; 4) predicted radiated pressure at r=1 m from the tunnel exit in dB. . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Predicted radiated pressure spectrum (sound pressure level, SPL) in dB by using a Gaussian approximation of the pressure gradient (blue line) and measurements from experiments (red line). . . . . . . . . . . . . . 2.6.1 Scheme of the set-up components: speaker (1), microphones (2), signal generator (3) and computer (4). . . . . . . . . . . . . . . . . . . . . . . iii. 2 4 12. 20. 21. 21 23 24 25 28. 31. 31 32.

(9) iv. List of Figures. 2.6.2 Variation of the pressure gauge P (in arbitrary units) with time t. Theoretical signal (blue line), actual signal reproduced by the high-speaker (red line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Scheme exits A1 and A2. Side view. . . . . . . . . . . . . . . . . . . . 2.6.4 Mounting of the porous exit A1. . . . . . . . . . . . . . . . . . . . . . . 2.6.5 Mounting of the porous exit A2. . . . . . . . . . . . . . . . . . . . . . . 2.6.6 Mounting of the PVC porous exit A2. . . . . . . . . . . . . . . . . . . 2.6.7 Tube with flanged open end. . . . . . . . . . . . . . . . . . . . . . . . . 2.6.8 Perforated cylindrical section. . . . . . . . . . . . . . . . . . . . . . . . 2.6.9 Area section of the horns. . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.10 Intermediate adapter and semi-cylindrical exits (B1, B2, B3, B4 and B5). 2.6.11 Mounting of the B1 exit. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.12 Mounting of the airshaft Sc /Sh = 1. . . . . . . . . . . . . . . . . . . . . 2.6.13 Adapter for airshaft of different sections. . . . . . . . . . . . . . . . . . 2.6.14 Pressure gauge on the train and inside the tunnel with an airshaft of area section 12 m2 at 350 m from the entrance in a tunnel of 90 m2 crosssection area, train speed 241 km/h. . . . . . . . . . . . . . . . . . . . . 2.6.15 Scheme of the ducts exit porosity distribution. . . . . . . . . . . . . . . 2.6.16 Porous duct exits of porosity 0.18 %, 0.42 % and 1.16 % tested at TU Berlin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.17 Experimental set-up to implement the TMTC technique using an aluminum exit of porosity σ = 1.16%. . . . . . . . . . . . . . . . . . . . . 2.7.1 a) Variation with the area ratio Sc /St of effective pressure transmitted by the airshaft RIT H multiplied by the inverse of the area ratio. Continuous line: results of Baron et al. [2001], circles: measurements. b) Variation with the area ratio St /Sc of the pressure wave reflection coefficient at the junction between the duct and the airshaft coefRT , transmitted through the duct coefT T , and transmitted to the airshaft coefT C . . . . . . . . . . 2.7.2 Variation with time t of pressure P (arbitrary units) of the incident wave OI (blue line) and the reflected wave OR (red line) at the PVC perforated exit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.3 Reflection coefficient at the perforated exit as a function of the number of holes opened, for flanged and unflanged exits. . . . . . . . . . . . . . 2.7.4 Influence of the open hole as a function of the distance to the exit for different frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.5 Variation with frequency f of the reflection coefficient R(f ) for exit samples with porosity σp 0.18, 0.42 and 1.16 % obtained with TMTC method, compared with flanged and unflanged analytical expression, and experiment results obtained with pulse reflectometry. . . . . . . . . . . . 2.7.6 Sound pressure level, SPL [dB] radiated from the duct end by hoods with different porosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Schematic representation of aerodynamic forces and the angle of attack, α, pitch angle of the velocity, γp , pitch angle of the body, θ; z, x is the inertial reference frame and zb , xb is the reference frame attached to the body. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 33 34 34 34 35 35 35 36 36 37 37. 38 41 42 42. 44. 45 46 47. 48 49. 54.

(10) List of Figures. 3.2.2 Variation of the dimensionless extracted power averaged per cycle, pe , A∗ A∗ with the relative amplitude of the motion, ∗ . ∗ is the relative U U pemax amplitude that provides maximum extracted power. . . . . . . . . . . . A∗ 3.2.3 Variation of b1 with the relative amplitude ∗ . a) Possible equilibrium U solutions: 1) one solution, 2) 3 solutions, 3) limit case. E: stable, I: unstable. b) no inflection points (case 1); one inflection point (case 2). . . 3.2.4 Determination of the maximum dimensionless extracted power from experimental results. a) Variation of dimensionless extracted power, pe , as A∗ a function of relative amplitude, ∗ , for two values of the pitch angle θ, U b) Variation of maximum extracted power, pemax , with the pitch angle of the body, θ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Variation of coefficient, b1 , with the relative amplitude, A∗ /U ∗ . Comparison of the analytical solution, b1a , and the numerical integration, b1n , for different curves of Cz (polynomial functions) around α = 0◦ , for the cases k according to Table 3.2.1. Discretization Δα = 1◦ . . . . . . . . . 3.2.6 Variation of coefficient, b1 , with the relative amplitude, A∗ /U ∗ . Influence of the discretization interval, Δα, of the force coefficient, Cz , in the numerical integration of b1 . Case k = 3 of Table 3.2.1. . . . . . . . . 3.2.7 Variation of the uncertainty in the relative amplitude at the equilibrium, disc , as a function of the discretization interval Δα of the curve Cz (α). Case k = 3 of Table 3.2.1. . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8 Variation of the transverse force coefficient, Cz , with the pitch angle of the body, θ. Symbols: pitch angles analyzed in Figure 3.2.9. Case k = 1, see Table 3.2.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.9 Variation of the transverse force coefficient, Czd (α), considering different pitch angles, θ0 , and the antisymmetric function, Czda , used in the numerical integration of b1 . Case k = 1, for θ0 angles shown in Figure 3.2.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A∗ 3.2.10 Variation of coefficient b1 with the relative amplitude ∗ , obtained by U numerical integration, b1n , at configurations with pitch angle θ0 = 0, and b1 analytic, b1a . Discretization interval Δθ = 1◦ . Case k = 1 in Table 3.2.1. For values of θ0 see Figure 3.2.8. . . . . . . . . . . . . . . . . . . A∗ 3.2.11 Variation of coefficient b1 with the relative amplitude ∗ , obtained by U numerical integration, b1n , at configurations with pitch angle θ0 = 0, and analytical solution, b1a . Discretization interval Δθ = 4◦ . . . . . . . . . . 3.2.12 Variation with the discretization interval Δθ of the standard deviation, σb1 , between the analytic solution b1a and the numerical integration b1n due to the discretization of Cz , for different pitch angles θ0 . Case k = 1 in Table 3.2.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Wind tunnel A4C: a) Instrumentation; b) Detail of the ATI six-component strain-gauge balance (model Gamma SI-130-10). . . . . . . . . . . . . 3.3.2 Wind tunnel A9: a) Instrumentation; b) Detail of the ATI six-component strain-gauge balance (model Delta FT5575). . . . . . . . . . . . . . . . 3.4.1 Nomenclature in the case of a biconvex airfoil. . . . . . . . . . . . . . .. v. 58. 59. 59. 61. 61. 62. 63. 63. 64. 64. 65 66 66 67.

(11) vi. List of Figures. 3.4.2 Variation with the pitch angle of the body, θ, of the coefficients of lift, cl , and drag, cd , and of the Glauert-Den Hartog parameter, H, over the biconvex airfoil of relative thickness Er =0.817 in the A4C wind tunnel. Symbols indicate the pitch angles θ0 considered in the analysis of Figures 3.4.3 and 3.4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Variation of the force coefficient, Cz , with the angle of attack, α, where α = θ − θ0 , for different values of pitch angle θ0 , around θ0 = 70◦ = 1.221 rad. Curve Cz interpolated, CzI , and its antisymmetric part, CzIa , for the biconvex airfoil of relative thickness Er =0.817. . . . . . . . . . A∗ 3.4.4 Variation with the relative amplitude ∗ of the coefficient b1n from the U numerical integration, and the specific dissipated energy, p̃d , for a biconvex airfoil of relative thickness Er =0.817 oscillating around a pitch angle of the body θ0 = 1.221 rad = 70◦ . . . . . . . . . . . . . . . . . . 3.4.5 Variation of the relative amplitude of equilibrium A∗ /U ∗ |eq as a function of the pitch angle, θ, for a certain specific dissipated power, p̃d , obtained from the parameters in Table 3.2.2. . . . . . . . . . . . . . . . . . . . . 1 3.4.6 Variation of the maximum specific extracted power p̃emax = b1 |max , as 2 a function of the pitch angle of the body, θ. . . . . . . . . . . . . . . . . 3.4.7 Variation of the maximum dimensionless extracted power, pemax , as a function of the pitch angle of the body, θ. . . . . . . . . . . . . . . . . . 3.4.8 Nomenclature in the case of the D-shape body. . . . . . . . . . . . . . . 3.4.9 Variation with the pitch angle of the body, θ, of the coefficients of lift, cl , and drag, cd , and Glauert-Den Hartog parameter, H, over the D-shape body tested in the A9 wind tunnel. Symbols indicate the pitch angles θ0 included in the analysis (see Figure 3.4.10). . . . . . . . . . . . . . . . . A∗ 3.4.10 Variation with the relative amplitude ∗ of the coefficient b1n obtained U from the numerical integration and the dissipation, p̃d , for the D-shape body, oscillating around a pitch angle of the body close to θ = 80◦ = 1.4 rad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.11 Nomenclature in the case of the rhomboidal cross-section airfoil. . . . . 3.4.12 Variation with the pitch angle of the body, θ, of the coefficients of lift, cl , and drag, cd , and Glauert-Den Hartog parameter, H, over the rhomboidal airfoil Er = 11/30 tested in the A9 wind tunnel. Symbols indicate the pitch angles θ0 included in the analysis (see Figure 3.4.13). . . . . . . . A∗ 3.4.13 Variation with the relative amplitude ∗ of the coefficient b1n obtained U from the numerical integration, and the dissipation p̃d , for the rhomboidal airfoil of Er = 11/30 around θ = 23◦ = 0.40 rad tested in the A9 wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.14 Variation with the pitch angle of the body, θ, of the coefficients of lift, cl , and drag, cd , and Glauert-Den Hartog parameter, H, over the rhomboidal airfoil Er = 10/30 tested in the A9 wind tunnel. Symbols indicate the pitch angles θ0 included in the analysis (see Figure 3.4.15). . . . . . . . A∗ 3.4.15 Variation with the relative amplitude ∗ of the coefficient b1n obtained U from the numerical integration, and the dissipation p̃d , for the rhomboidal airfoil of Er = 10/30 around θ = 23◦ = 0.40 rad tested in the A9 wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68. 68. 69. 69 70 70 71. 71. 72 72. 73. 73. 74. 74.

(12) List of Figures. 3.4.16 Variation with the pitch angle of the body, θ, of the coefficients of lift, cl , and drag, cd , and Glauert-Den Hartog parameter, H, over the rhomboidal airfoil Er = 12/30 tested in the A9 wind tunnel. Symbols indicate the pitch angles θ0 included in the analysis (see Figure 3.4.17). . . . . . . . A∗ 3.4.17 Variation with the relative amplitude ∗ of the coefficient b1n obtained U from the numerical integration, and the dissipation p̃d , for the rhomboidal airfoil of Er = 12/30 around θ = 23 = 0.40 rad tested in the A9 wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.18 Variation with the pitch angle, θ, of the maximum dimensionless extracted power, pemax , for different cross-section bodies. . . . . . . . . . 3.4.19 Variation with the pitch angle, θ, of the maximum specific extracted power, p̃emax , for different cross-section bodies. . . . . . . . . . . . . . . 3.4.20 Variation of the transverse force coefficient, Cz with the angle of attack, α, experimental data from Ng et al. [2005], Parkinson and Smith [1964], Luo and Bearman [1990] and Parkinson and Brooks [1961]. In this Figure, the 9th and 11th order polynomials of Ng et al. [2005] are coincident. A∗ 3.4.21 Variation with the relative amplitude ∗ of the coefficient b1 obtained U by direct numerical integration of experimental data, b1ne ; by integration of a 7th order polynomial, b1n7 ; and the specific dissipated power, p̃d , for a square-cylinder. Polynomial coefficients (a1 = 2.69, a3 = −168, a5 = 6270, a7 = 59900 at Re∼ 22300) from Parkinson and Smith [1964]. . . . A∗ 3.4.22 Variation with the relative amplitude ∗ of the coefficient b1 obtained U by direct numerical integration of 7th, 9th and 11th order polynomial, b1n7 , b1n9 and b1n11 , respectively; experimental data, b1ne ; and the specific dissipated power, p̃d , for a square-cylinder. Experimental data and polynomial coefficients extracted from Ng et al. [2005]. . . . . . . . . . 3.4.23 Variation of the transverse force coefficient Cz , with the angle of attack α (from Parkinson and Brooks [1961]) and 7th, 9th and 11th order polynomials that fit the experimental data, obtained with a Matlab function (polyfit), see Table 3.4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . A∗ 3.4.24 Variation with the relative amplitude ∗ of the coefficient b1 obtained U by numerical integration of 7th, 9th and 11th order polynomial, b1n7 , b1n9 and b1n11 , respectively; experimental data, b1ne ; and the specific dissipated power, p̃d , for a square-cylinder. The lift cl and drag cd coefficients to obtain Cz were taken from Parkinson and Brooks [1961], and Cz (α) is shown in Figure 3.4.23. . . . . . . . . . . . . . . . . . . . . . 3.4.25 Damper device based on transverse galloping with active magnetic suspension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 DLF of a common trimmed interior cavity of a vehicle. . . . . . . . . . 4.2.2 Two plates connected through a point junction. . . . . . . . . . . . . . . 4.2.3 Mobility Y = |v/F | of a common structure used as floor in high speed trains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Variation with frequency of the TL of a panel . . . . . . . . . . . . . . . 4.2.5 Open field vibro-acoustic models. . . . . . . . . . . . . . . . . . . . . . 4.2.6 TL of structures parts of the train. . . . . . . . . . . . . . . . . . . . . . 4.2.7 Some of the DLFs used in the SEA structural subsystems. . . . . . . . .. vii. 75. 75 76 76. 77. 77. 78. 78. 79 80 89 89 90 91 94 96 97.

(13) viii. List of Figures. 4.2.8 Modal densities of the FEM structural parts prone to be substituted by SEA subsystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2.9 Analysis of modal density and radiation loss factor of train roof to interior and exterior acoustic cavities. . . . . . . . . . . . . . . . . . . . . . 98 4.2.10 CLFs to exterior and interior cavities from wagon roof and floor. . . . . 98 4.2.11 Difference on CLFs depending on panel excitation. . . . . . . . . . . . . 99 4.2.12 SEA vibro-acoustic models: a) 2 wagons, b) section model. . . . . . . . 99 4.2.13 a) SPL (dB) predicted numerically with the one section model in the interior and exterior acoustic cavity in 23 m from the nose of the train, due to the relocated load of converter at 29 m and TBL of the whole train; b) SPL (dB) in the interior and exterior of the section at 23 m, due to all the loads in this section and the relocated loads of the converter at 29 m and the TBL of the rest of the train. . . . . . . . . . . . . . . . . . 100 4.2.14 Continuity of vibro-acoustic models. . . . . . . . . . . . . . . . . . . . 100 4.2.15 Cross-sections of a) extruded structure Z-shape and b) equivalent flat plate.101 4.3.1 Microphones locations and sections instrumented with accelerometers. . 103 4.3.2 Accelerometers placement layout around the window frame. . . . . . . . 103 4.4.1 SPL (dB) in the microphones at 300 km/h in open field: a) at the head; b) at the tail. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.4.2 SPL (dB) in the microphones a) at the head b) at the tail at 300 km/h inside a tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.4.3 Low frequency noise inside the tunnel. SPL spectrum of microphones averaged M6 , M5 , M4 and accumulated M6a , M5a , M4a . . . . . . . . . . 106 4.4.4 Sound pressure level spectra in thirds of octave bands considered in the vibro-acoustic model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.4.5 Acceleration spectral density in the junctions at 300 km/h. . . . . . . . . 107 4.4.6 Transmissibility obtained from the accelerometers at 300 km/h [SorribesPalmer et al., 2014]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.5.1 SPL (dB) predicted inside the train at 300 km/h in a section at 25 m from the nose: a) analytic expression for CLF in point junction b) point junction CLF obtained from experimental test. . . . . . . . . . . . . . . 108 4.5.2 SPL inside the train for attached and detached flow configuration at different speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.5.3 SPL inside the train at 11 meter from the nose at speed: a) 300 km/h b) 350 km/h. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A.1.1 Wave separation using the method proposed in Kikuchi et al. [2009]. . . 127 A.1.2 Wave separation using the proposed method. . . . . . . . . . . . . . . . 128 A.2.1 Geometry of the considered horns. The length l has been chosen to be 2.4 times the height h of the section at the exit. . . . . . . . . . . . . . 129 A.2.2 Variation of the transmission coefficient τ with the Helmholtz number of conical, exponential and catenoidal horns. . . . . . . . . . . . . . . . 130 A.3.1 Undesired reflection at a junction. . . . . . . . . . . . . . . . . . . . . 133 A.3.2 Tube with unflanged open end. . . . . . . . . . . . . . . . . . . . . . . 133 A.3.3 Tube with flanged open end. . . . . . . . . . . . . . . . . . . . . . . . . 133 A.3.4 Variation of the reflection coefficient at the duct exit with the Helmholtz number (ka), compared with the expression proposed in Silva et al. [2009].134.

(14) List of Tables. 2.3.1 Train properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Area of holes of exit A2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Horn dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Temperature corrections in the air properties [Flecher and Rossing, 1991]. . . 2.6.4 Scheme of pressure measurements during microphones position exchange. Fe is the scale factor; αa : plane wave attenuation coefficient; Poa and Pob : reference pressure of cases a and b, respectively. . . . . . . . . . . . . . . . . 2.6.5 Scale factor, Fe , attenuation coefficient, αa , inside the PVC tube for different distances between the microphones s. . . . . . . . . . . . . . . . . . . . . . 2.6.6 Frequency ranges under analysis in the different experimental set-ups. The distance between the microphones used in the TMCT was s = 76.5 mm. . . . 2.6.7 Diameter radius Φ, and porosity σp , of the samples tested with the TMTC technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.1 Ratio between the reflection coefficient in the horns and the horn B1. . . . . . 2.7.2 Transmission loss (TL) through a porous section. . . . . . . . . . . . . . . . 2.7.3 Reflection coefficient at the perforated exit R for different number of open holes in the unflanged perforated exit. . . . . . . . . . . . . . . . . . . . . . 2.7.4 Reflection coefficient at the perforated exit, R, as a function of the number of open holes in the flanged perforated exit. . . . . . . . . . . . . . . . . . . . .. 24 33 36 39. 39 40 40 41 43 45 46 46. 3.2.1 Polynomial coefficients used in the validation of the numerical integration method, extracted from Barrero-Gil et al. [2009] for different cases k. . . . . 60 3.2.2 Values used to estimate the specific dissipation power, pd , extracted from Alonso et al. [2012]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.4.1 Coefficients of 7th, 9th, 11th order polynomials obtained with Matlab function polyfit for the fitting of the experimental data Cz (α) obtained from Parkinson and Brooks [1961]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.1 Definition of lower, center and upper frequencies in 1/n-th of octave frequency bands. n is the desired fraction of octave (n must be an integer greater than or equal to 1), m is the index of the band (m can be a positive, zero or negative integer), and f0 is a fixed reference frequency (set to 1000 Hz). . . . 86 4.2.2 Energy and modal density of SEA subsystems [Wijker, 2009]. . . . . . . . . 92 ix.

(15) x. List of Tables. 4.2.3 Models material properties. HPL: High Pressure Laminate; SMC: Sheet Molding Compound; EPDM: Ethylene Propylene Diene Monomer; PVB: Polyvinyl Butyral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Foam properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Methods used to model, depending on the frequency range. . . . . . . . . . 4.2.6 Pressure rout mean square for attached and detached flow. . . . . . . . . . . 4.2.7 TBL power spectral density parameter. . . . . . . . . . . . . . . . . . . . . 4.3.1 Accelerometers used in test campaign. . . . . . . . . . . . . . . . . . . . . 4.4.1 Measured SPLOA (dB) in open field at 300 km/h, with x being the microphone location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 SPLOA (dB) inside the tunnel at 300 km/h, with x being the microphone location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. 94 94 95 102 102 104. . 105 . 105. A.2.1The transmission coefficient τ of conical, exponential and catenoidal horns [Morse, 1948]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.3.1Influence in the reflection coefficient R of microphone M2 insertion into the duct. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.3.2Influence of the leakage through the duct holes. . . . . . . . . . . . . . . . . A.3.3Expression to estimate the pressure attenuation taking into account humidity variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 130 131 131 132.

(16) Nomenclature. Roman Symbols A. Oscillation amplitude [m]. Atr. Cross-sectional area of the train [m2 ]. Atun. Cross-sectional area of the tunnel [m2 ]. b. Characteristic dimension of the body in the direction transverse to the flow [m]. b1a. Analytic determination of b1. Bp. Bending stiffness of a plate [N · m2 ]. bn. n-th polynomial coefficient of the sinus series expansion of Cza. b1n. Numerical determination of b1. cf tr. Friction coefficient of the train. cf tun Friction coefficient of the tunnel fc. Coincidence frequency [Hz]. cp. Specific heat at constant pressure [J/(kg · K)]. c. Free field sound speed propagation in the air [m/s]. Cz. Dimensionless coefficient of the aerodynamic force transverse to the flow. Cza. Antisymmetric part of the dimensionless force coefficient Cz. Czd. Dimensionless force coefficient, body pitch angle displaced from origin. Czda. Antisymmetric part of the dimensionless force coefficient, body pitch angle displaced from origin, Czd. Dtun Tunnel diameter [m] Qθ. Directivity. r. Distance [m] xi.

(17) xii. List of Tables. E. Young modulus [Pa]. f. Frequency [Hz]. fcenter Central frequency of the band [Hz] fl. Lower frequency of the band [Hz]. fu. Upper frequency of the band [Hz]. fv. Vortex shedding frequency [Hz]. fz. Aerodynamic force in the direction transverse to the flow [N/m]. cg. Group speed [m/s]. H. Glauert-Den Hartog parameter. H12. Transfer function between microphones pressure spectra. H2. Transfer function between accelerometer power spectral density. Z. Acoustic impedance [Pa · s/m]. k. Wave number [rad/m]. L. Characteristic dimension of the structure in the flow direction [m]. Lx. Characteristic length in x direction [m]. Ly. Characteristic length in y direction [m]. M. Mach number. Imax. Maximum sound intensity [Pa · m/s]. Y. Mobility [s/kg]. n(ω) Modal density [mode/Hz] M (ω) Modal overlap [mode/Hz] Ixx. Momentum of inertia in x axis [kg · m2 ]. pemaxt Absolute maximum dimensionless extracted power, averaged per cycle cph. Phase speed [m/s]. Pd. Dissipated power, averaged per cycle [W/m]. pd. Dimensionless dissipated power, averaged per cycle. pd. Dimensionless dissipated power, averaged per cycle and per maximum relative amplitude (specific dissipated power).

(18) List of Tables. xiii. Pe. Extracted power, averaged per cycle [W/m]. pe. Dimensionless extracted power, averaged per cycle. pe. Dimensionless extracted power, averaged per cycle and per maximum relative amplitude (specific extracted power). Pr. Prantdl number. prms. Pressure root mean square [Pa]. q. Dynamic pressure [Pa]. a. Inner radius of the cylindrical duct [m]. Re. Reynolds number. R. Reflection coefficient. Rc. Room absorption constant. Sc. Scruton number. St. Strouhal number. S. Surface [m2 ]. T. Oscillation period [s]. t. Time [s]. tr. Characteristic residence time [s]. TR. Reverberation time [s]. tv. Time scale of the structure oscillations [s]. Utr. Train speed [m/s]. U∗. Dimensionless velocity of the incident flow. U. Velocity of the incident flow [m/s]. V. Volume [m3 ]. z0. Transverse displacement to the incident flow [m]. Acronyms BEM Boundary Element Method CAA Computational Aeroacoustics CLF. Coupling Loss Factor.

(19) xiv. List of Tables. DAF Diffuse Acoustic Field DES Detached Eddy Simulation DG. Discontinuos Galerkin. DLF Damping Loss Factor DNS Direct Numerical Simulation EPNL Effective Perceived Noise Level EPDM Ethylene Propylene Diene Monomer FEM Finite element method FSP. Fluctuating Surface Pressure. FWH Ffowcs-Williams and Hawkings HPL High Pressure Laminate HVAC Heating, Ventilation and Air Conditioning LBM Lattice-Boltzmann Method LEE. Linearized Euler Equations. LES. Large Eddy Simulation. NCT Noise Control Treatment PVB Polyvinyl Butyral PSD. Power Spectral Density. RANS Reynold Averaged Navier Stokes equations RMR Rock Mass Rating ROR Rain On the Roof SEA Statistical Energy Analysis SMC Sheet Moulding Compound SIF. Semi-Infinit Fluid. SIL. Speech Interfeence Level. SPL. Sound Pressure Level. TBL Turbulent Boundary Layer TL. Transmission Loss. TNS Train Nearfield Signature TWS Train Wave Signature.

(20) List of Tables. xv. URANS Unsteady Reynold Averaged Navier Stokes equations WBM Wave-Based Method Greek Symbols α. Angle of attack [rad]. αa. Sound absorption coefficient [dB/m]. αav. Average absorption coefficient. φ. Blockage ratio between the train and the tunnel area sections. η. Dynamic viscosity of the air [kg/(m · s)]. ηs. Acoustic radiation loss factor. ηb. Border loss factor. ηs. Structural loss factor. γ. Heat capacity ratio of the air. γp. Pitch angle of velocity [rad]. κ. Thermal conductivity [W/(m · K)]. ν. Poisson modulus. ω. Angular frequency [rad/s]. ωn. Undamped natural frequency [rad/s]. ω0. Oscillation frequency of the structure [rad/s]. Δpf r Pressure gauge due to friction effects caused by the entry of the main part of the train into the tunnel [Pa] ϕ. Phase between oscillations and the aerodynamic force transverse to the flow [rad]. ΔpHP Pressure gauge caused by the passing of the train head at the measurement position in the tunnel [Pa] ΔpN Pressure gauge caused by the entry of the nose of the train into the tunnel [Pa] ΔpT. Drop in pressure caused by the entry of the tail of the train in the tunnel [Pa]. ρ. Air density [kg/m3 ]. ρs. Structure density [kg/m3 ]. σ. Radiation efficiency. τ. Dimensionless time. τ. Transmissibility.

(21) θpemaxt Pitch angle of the body at absolute maximum extracted power [rad] θ. Pitch angle of the body [rad]. σ. Porosity. ζ. Dimensionless structural damping coefficient. Note: Realize that sometimes the same symbol has been used to refer different variables or parameters. It has been done this way to use the traditional nomenclature used in bibliography..

(22) Chapter 1 Introduction. 1.1. Noise sources in high speed trains. In the last years the effort invested on the study of high speed trains aerodynamics has increased considerably. Among the main objectives of research, there is the improving of the comfort of train passengers and of the citizens of the tunnel portals surrounding infrastructure. Reducing the minimum tunnel cross-section needed for high speed trains passing through without decreasing their speed has been one of the main topics in railway infrastructure research, because of its impact on construction costs. As train speed has been increasing, the aerodynamic noise has become one of the main train noise sources, and at the same time the center of attention of many researchers. A classical review of the main aerodynamic and aeroacoustic problems of high-speed trains and the strategies followed to alleviate their undesirable effects can be found in Raghunathan et al. [2002]. This paper summarizes the studies performed on the comfort and safety of the passengers and the environment of the train, aerodynamic drag, pressure variations inside train, train-induced flows, cross-wind effects, ground effects, pressure waves inside tunnel, impulse micro-pressure waves at the exit of tunnel (MPW), noise and vibration generated by the train, and its energy consumption. It also presents some expressions to estimate: the trains aerodynamic drag, the pressure gauge of the compression wave generated at the entrance during the train entering in a tunnel, and also the impulsive micro-pressure wave which is radiated outside when the pressure wave reaches the tunnel exit. Another good review of the main sources of noise and vibration on railways, and the concepts needed to understand the physics involved is presented in Thompson [2009]. As it can be appreciated in Figure 1.1.1, special attention should be paid to aerodynamic noise. It should be pointed out that the square of the acoustic pressure depends on the 6th power of the Mach number, M = Utr /c, as p̄2 ∝ Aρ2 c4 M6 [Curle, 1955], which is dominant above 300 km/h. Aerodynamic noise is caused by the flow of air over the train as it travels at high speed. Near the train nose the boundary layer is laminar, but due to viscosity effects it turns into turbulent. This transition depends mainly on the train surface roughness, negative 1.

(23) 2. CHAPTER 1. INTRODUCTION. pressure gradients, free-stream disturbances and on the Reynolds number Re = ρUtr L/μ. The Reynolds number of the flow around a train of 3.5 m height traveling at a speed of Utr = 300 km/h is about Re ∼ 2 · 107 . Crespi et al. [1994] measured the boundary layer on a high speed train at different speeds using laser Doppler velocimeter mounted on board. The measurements showed that thickness is relatively constant along the train (some 2 m), and that it increases rapidly towards the lower region of the vehicle due to ground friction and blocking effect of the bogie.. Aerodynamic noise ~U6 Wheel/rail interaction noise ~U4 1. Lw [dB]. Engine/generator noise ~U Total. 1. 10. Utr [km/h]. 10. 2. Figure 1.1.1: Variation of the sound power levels Lw with train speed Utr of different sound sources (after Lauterbach et al. [2012]). Broad-band noise generated by wheel-rail interaction is clearly dominant at middle speeds. The vibration excited by the contact between the wheel and the rail is highly dependent on the surface irregularities. Squeal noise generated by the wheels during the curves of tight radius is high pitched tonal and can be quite annoying, as well as the impact noise that can appear at discontinuities in the track or the wheel (rail joints, points and crossings). Dominant frequencies of ground-borne vibration can be between 4 and 50 Hz for soft soil, and between 30 and 200 Hz inside a tunnel due to the radiation by vibration of their walls, and can increase the overall level of noise up to 20 dB when crossing through a bridge. The cross wind can increase drag and also moves forward the detachment point of the boundary layer over the train surface, which dramatically increases the aerodynamic noise. A study of the flow around high speed trains (around train nose, a long the side, roof, underbody and the wake) with special attention to cross winds is presented in Baker [2010]. The dominant sources of aerodynamic noise in high speed trains are typically dipoletype. Cavity noise which appear between the train inter-coach gap can be an important source of noise, and the tonal frequencies can be predicted by Rossiter’s equation [Rossiter, 1964]. Other important tonal sources can be the wake generated by the pantograph, roof-mounted equipment, ventilation grilles, etc. The Strouhal number St = f L/U can be of help to identify the characteristic length L of the shedding vortices that.

(24) 1.1. NOISE SOURCES IN HIGH SPEED TRAINS. 3. can appear in the pantograph. If the mean flow velocity U and the frequency are known, assuming St ∼ 0.2 (as is the case for a cylinder above Re > 3 · 105 ) the characteristic length can be estimated. The tonal frequency for a typical pantograph diameter of 3 cm at 300 km/h is close to 500 Hz. Array microphone measurements in free field or in aeroacoustic wind tunnels have been used successfully to identify the main aeroacoustic sources, but quantification of sources strengths remains still difficult due to contamination from other sources, background noise, etc. The optimization of the methods for analysis and post-processing like beam-forming (least mean square), deconvolution (CLEAN-SC based on source coherence), diagonal removal, BiClean algorithm, etc.) are in the center of attention of many researchers. Among the assumptions considered in beam-forming for the characterization of the aerodynamic noise in a train are: the sound sources are located in a plane to the side of the train, all sources are incoherent and they are statistically time independent. Vertical disposition of the microphones are used to find the height of the source meanwhile the horizontal array is used to locate their position along the train. Besides the flow-induced noise caused by turbulence and unsteady flows, another mechanism of sound generation is the vibration of solid bodies (structure-borne sound) which can also generate and radiate sound energy. Meanwhile the fluids can only store energy in compression (longitudinal waves), the solids can store energy in compressional, flexural (transverse or bending), shears and torsional waves. But flexural (bending) waves are the only type of structural wave that plays a direct part in sound radiation and transmission [Norton and Karczub, 2003]. The junctions between the structures and the noise control treatments applied in structures (vehicle floor, walls, windows, doors and roof) play an important roll in the path in which the energy flows between them and the environment. Noise from the air-conditioning system can also require consideration in modern trains as there is often very limited space in which to package the air-conditioning unit and ducts [Thompson, 2009]. Also fixing equipment, such as compressors under the floor structure, or a carriage on the roof, can transmit energy to the train interior by both airborne and structure-borne paths, as shown in the scheme of the main sources in Figure 1.1.2. Mounting stiffness must be carefully chosen in accordance to the characteristic load, this combined with a good mounting practice can reduce significantly noise transmission. Avoiding leaks during the mounting process is critical to reduce direct airborne transmission. High speed trains passing by each other or by stationary structures produce also important effects to be taken into account in the design process of the train. All this aerodynamics effects must be studied to optimize the train shape. For example, if a high speed train with two floor levels is wanted to be built, a compromise must be achieved between the cross-section needed to fit the 2 levels, the aerodynamic resistance (which influences critically in the power consumption), the overturning moment due to crosswinds, the maximum speed to enter in the tunnels railways in which it is going to be operated, the surface section prone to flow detachment, etc..

(25) 4. CHAPTER 1. INTRODUCTION . . . . Figure 1.1.2: Main sources of interior noise in a train and their transmission paths into the vehicle (after Thompson [2009]). In Spain, the infrastructure for high speed trains has experienced a considerable increase over the last 10 years, a big part of the resources have been invested in railway tunnels construction. Inside tunnels, the noise level transmission of rolling noise and aerodynamic noise increase, specially the one generated in the inter-coach gap. A decrease of the tunnel cross-section area can save several MC, and this can be achieved studying the critical situations that can occur in the tunnel during the train passing through. The tunnel portals, at both the entrance and exit, play an important role reducing not just the pressure gradient of the waves generated by the train but also the intensity of the pressure gauge during the reflection process. The reflection of pressure waves at tunnel entrance/exit is analyzed in this work both numerically and experimentally. The reflection of step-wavefronts from perforated exits was studied in Vardy [1978], comparing it with the reflection at a flared portal, concluding that flared is less advantageous than a perforated exit. This paper also highlights that unacceptable pressure gradients will remain unless very long extension of portal hoods are used, and even that will not solve the problem due to pressure transients and non-linear effects. This study leads to the conclusion that is important to attenuate the pressure wave before it reaches the tunnel exit. To do this some used mechanisms are: tunnel side branches [William-Louis and Tournier, 1998], increasing tunnel friction (ballast track is not feasible in long tunnels), using Helmholtz resonator (acoustic liners are commonly used in aircraft engine noise reduction), extracting energy from the pressure waves using appropriated devices, etc. An extensive review on noise reduction methods that could be considered to be applied in railway tunnels can be found in Ingard [2008]. A good review of aerodynamic instabilities like galloping, vortex-induced vibration,.

(26) 1.1. NOISE SOURCES IN HIGH SPEED TRAINS. 5. wake-induced instabilities, etc., can be found in Paidoussis et al. [2011]. Transverse galloping is an aerodynamic instability that can appear in slender structures with non-circular sections, with oscillation amplitudes in cross-wind direction, like in electrical lines after ice deposition, traffic signals, bridge decks, etc. The residence time of a fluid particle is small compared to the period of the oscillating body, so the hypothesis of quasi-steadiness can be assumed, and static pressure measurements can be used to characterize the dynamic behavior. The amplitude of oscillations are limited by non-linear aerodynamic effects, which establish a oscillation limit cycle [Barrero-Gil, 2008], this makes easier the fatigue and damage tolerance estimations of the device. This properties and the fact that the magnitude of the flow velocity induced by the pressure waves generated by a train inside a tunnel is of the order of the transverse galloping critical wind speed, make from transverse galloping a phenomenon easy treatable both analytically and experimentally, which could also be implemented in tunnel railways airshaft, portals, etc. The aerodynamic phenomena during the entering of the train into a tunnel were treated theoretically in Hara [1961]. In this paper the velocities and pressures in each portion of the tunnel are calculated, also an expression for the pressure drag is obtained under the assumption of compressible and inviscid air. The compression wave transient and its reflections in the tunnel portal during the train passing through it are studied numerically in Zeng and Gretler [1995]. A theoretical model for the pressure field in a tunnel generated by high speed train, modeled by a pair of moving monopoles into a semi-infinitely long tunnel, is presented in Sugimoto and Ogawa [1997], the model is validated with CFD by solving directly the Euler equations for inviscid and compressible air. An analytical study of the compression wave generated by a train entering a tunnel and the influence of the train nose geometry in the shape of the wave can be found in Howe [1997a]. In this analytical solution, the train is modeled by a uniformly translating continuous distribution of monopole sources whose density is proportional to the local gradient of the cross-section area of the train. The head wave is expressed as the convolution product of the sources and an acoustic Green’s function, whose determination is simplified at low Mach numbers when the characteristic thickness of the head wave is large compared to the tunnel diameter. Also a second dipole of comparable strength is attributed to “vortex sound” sources in the shear layers of the black-flow out of the tunnel of the air displaced by the train. The intensity of the wavefront of the compression wave generated by the train can be estimated by using the train’s speed Utr , the blockage ratio, φ - which is the ratio of the cross-section area of the train, Atr and the tunnel, Atun - the nose profile of the train, the geometry of the tunnel entrance and the atmospheric conditions (density, ρ and temperature T of the air). The influence of the Mach number (M = Utr /c) is studied in Howe [1997a], where the models are validated with published experimental measurements presented in Maeda et al. [1993]. The effect of vents in the tunnel entrance portal in the rise time of the wavefront to alleviate the impulsive micro-pressure radiation at the tunnel exit is analyzed in Howe [1998] and Howe [1999]. The maximum compression wave rise time that can be obtained with vents is equal to the time of passage of the front of the train through the perforated section. The Rayleigh’s method for the approximate calculation of potential flow from the open end of a semi-infinite flanged cylinder is applied in Howe [1999b] to obtain analytical representations of the Green’s function describing the generation of sound waves within a flanged cylinder by sources located in the neighborhood of the open end. The expression for the pressure rise across the wave front generated by the train en-.

(27) 6. CHAPTER 1. INTRODUCTION. tering in the tunnel is given approximately in Howe et al. [2000]. The amplitude of this pressure is typically 1-3% of the atmospheric pressure (around 150 dB) when the train Mach number exceeds about 0.2 (at 250 km/h). This paper proofs that a “flared” portal entrance hood without windows behaves as an ideal hood producing a linear increase in pressure with distance across the wavefront, with a constant pressure gradient that is as small as practicable, but also implies a great increase in construction costs and space requirements. The aerodynamic phenomena generated by a train in a tunnel is analyzed by onedimensional numerical simulation in several tunnel configurations in Baron et al. [2001]. A tunnel design criteria for long-range underground high-speed railways is established and also the positive and negative effects of pressure relief ducts and partial air vacuum are discussed. A reduce-scale (1/77) experimental set-up to study the compression wave generation is used in Bellenoue et al. [2002], and validated with 3-D simulation and full-scale test measurements. The generated compression wave is clearly established as a planar wave once it has propagated some four times the tunnel’s diameter inside the tunnel. So, the 3-D model can be replaced by a 2-D (axially symmetric) model, saving computational time. Meanwhile the optimal longitudinal cross-section area distribution of the train nose to increase the rise time of the compression wave in the tunnel can be estimated using axially symmetrical models, drag and aerodynamic stability optimization in open air must be performed by using 3-D models. The resistance coefficients of a train from full scale measurements inside tunnel during routine operation are calculated in Vardy and Reinke [1999]. We use this values in our implemented code to predict the pressure gauge due to friction. The vented hood as a method to reduce micro-pressure wave by increasing the time rise of the pressure was studied analytically in Howe [1998]. A theoretical analysis of the influence of the unvented hood geometry and its optimal size on the wavefront can be found in Howe et al. [2002]. The optimal distribution and size of the windows in a vented hood is studied in Howe et al. [2003]. The infrasound generated when a antisymmetric model of a train enters along the axis of a a duct is studied in Howe [2003c]. This lowfrequency pressure pulses generated by the train entering and leaving the tunnel, also known as tunnel continues waves (TCW), are also studied in Kikuchi et al. [2009]. Here an interesting method to separate the incident and reflected waves from pressure data measured inside tunnel is presented. The objective is to study the amount of energy of the incident wave which is radiated from the portal as micro-pressure waves. The influence of the train nose profiles in the generation of the wavefront is studied in Sato and Sassa [2005] numerically, together with an experimental set-up used to validate the results. The thickness of the wavefront can be made many times larger than its typical thickness order of 5 tunnel diameters Dtun , when the wave is reflected at a tunnel exit with a discrete distribution of rectangular widows as shown in Howe and Cox [2005]. The expansion wavefront reflected at the exit, and the expansion wave caused by the inward propagating pulses generated at the windows are shown for two different windows area distributions, one with equal area and another with linearly increasing area. A fast method to evaluate separately the different contributions to the compression wave generated by a high speed train entering a tunnel with vented hood is proposed in Howe et al. [2006]: the interactions of the train nose with the hood portal, the junction.

(28) 1.1. NOISE SOURCES IN HIGH SPEED TRAINS. 7. between the hood and the tunnel, the effect of the windows, and the contribution of the separated flow along the sides of the train. A genetically optimized tunnel-entrance hood (playing with the dimensions and distribution and sizing of the hood windows) in Howe [2007] with the aim to reduce the maximum pressure gradient is presented. The aerodynamic noise generated in the boundary layer over a high speed train has been widely studied with simulations using different numerical methods such as Susuki [2001], Wang et al. [2008], Muld [2012], etc. The methods used in aeroacoustics have experienced a very fast development due to the need of reducing the computational time of the simulations. Some of the numerical methods used on this field are the direct numerical simulation of the Navier Stokes equations (DNS), large eddy simulation (LES), Reynolds Averaged Navier Stokes equations (RANS) and unsteady RANS (URANS). Computational aeroacoustics (CAA) is developing new techniques to simulate the aerodynamic noise combining different methods. URANS could satisfy the need for grids in engineering problems, but it can lead to relatively large numerical error due to its failure in capturing the sources in sub-grid scales. In Sun et al. [2012] a nonlinear acoustics solver is used to reconstruct the unresolved sub-grid scales from a previous RANS simulation that provides an initial statistically-steady model of turbulent flow. Detached eddy simulation (DES) combines RANS formulation to simulate the adhered portion of the boundary layer with LES formulation for detached flow zone. The aeroacoustic noise generated in the bogie cavity is studied in Takaishi et al. [2002], where the three-dimensional unsteady flow around the train is solved by the LES technique and the distribution of dipole sound sources is predicted numerically by coupling the instantaneous flow properties with the compact Green’s functions. In Paradot et al. [2008] a LES simulation of aeroacoustic sources and their near-field propagation based on the Lattice-Boltzmann method (LBM) is computed. The far-field propagation and structural coupling is calculated using Ffowcs-Williams and Hawkings method (FWH), which used the aeroacoustic analogy [Lighthill, 1952], assuming that sound propagation follows the simple wave equation, which can be solved through the integration on the surface surrounding the nonlinear acoustic sources. This methodology that separates generation from propagation of sound is also used in Chen et al. [2011] to calculate the wind excitation in a car. Linearized Euler Equations (LEE) is also quite used when viscous effects can be considered 2nd order source of sound. A literature survey of the techniques used concerning the internal noise prediction is presented in Lalor and Priebsch [2007]. The common methods used to analyze sound transmission are classified in: finite element method, boundary element method, statistical energy analysis, hybrid methods, ray tracing methods and band-averaged transfer function method. This paper also introduces the main aspects to take into account in noise prediction modeling, like the mechanisms of internal noise generation: the direct transmission (“leakage”), the “mass law” and the acoustic radiation by vibration walls; also highlights the high influence of the damping in the spot-welded and bolted joints in the variability of internal noise in deterministic methods. Among the different techniques mentioned in this paper, FEM, BEM, the Wave-Based Method (WBM) and SEA are presented as the more widely used in interior noise prediction. Lightweight, large area structures, like structures used in high speed trains are very sensitive to acoustic loads. A combined FEM and BEM analysis is commonly used to simulate the fluid structure interaction at low frequencies, specially with exterior fluids. High order schemes used in finite difference methods are extremely sensitive to the generation of spurious high-frequency waves. Discontinuous Galerkin’s method, based on.

(29) 8. CHAPTER 1. INTRODUCTION. high-order polynomials basis functions is also used in CAA. In DG, fluxes between internal elements are calculated, solving an approximated Riemann problem [Lorenzoni, 2008]. SEA is suitable for problems that combine many different sources of excitation, whether mechanical or acoustic. In SEA the structural vibrational behavior of elements (subsystems) is described statistically. For high-frequencies a deterministic modal description of the dynamic behavior of structures is not very useful [Wijker, 2008]. The concept of SEA is simple: the structure or fluid is split up into subsystems characterized by its internal energy, its Damping Loss Factor (DLF) and its Coupling Loss Factor (CLF) which determine the efficiency by which energy is transmitted into vibrational power to its neighbours. If power from an external source is applied to a subsystem, part of the energy will be dissipated within the subsystem due to its damping and the rest will be transferred to the neighboring subsystems, a detail description can be found in Lyon and DeJong [1995]..

(30) 1.2. OBJECTIVES AND CONTENT STRUCTURE. 1.2. 9. Objectives and content structure. The objective of this work is to pay attention to and analyze several of the phenomena that takes place concerning the aerodynamic noise in high speed trains (pressure waves generated in the passing of a train through a tunnel, micro-pressure waves radiated from railway tunnel portals, noise generated aerodynamically around the train, etc) and to study some ideas to alleviate those problems as: mechanisms to reduce noise inside the train, the tunnel and the surroundings; methodologies to analyze aeroelastic instabilities; and on track measurements of aerodynamic noise. Among the acoustic problems analyzed in this work there is the generation, propagation of pressure waves inside tunnel and the micro-pressure radiated outside the tunnel. Several studies on the influence of the main parameters (tunnel portals geometry, track configuration, existence of airshafts, train shape, non-linear propagation) are performed and validated with measurements performed on track, data extracted from bibliography or with scale tests. These data are used in a semiempirical method to predict efficiently in the first steps of design the sound pressure level inside a high speed train using different approaches to characterize, analyze and reduce the airborne and structure borne noise. Vibro-acoustic models are used to analyze the influence of the modelization parameters. This dissertation is divided in five chapters, in the first chapter there is an introduction to the main sources of noise in high speed trains and their influence in passenger comfort and tunnel surroundings, together with a summary of the state of the art of the engineering techniques applied to evaluate and design countermeasures and some of the solutions adopted. In chapter 2 the problems associated to the pressure wave generated by the train entering a tunnel are considered. Among them are: the pressure wave propagation, the micro-pressure wave radiated outside the tunnel portals, the experimental setups built to study the pressure waves propagation, the influence of the hydrostatic pressure in the fulfillment of comfort and health standards, and an alternative indicator to evaluate passenger discomfort to be used in the standard is proposed. In chapter 3 a method to study the extraction of energy from the pressure waves that propagate inside the tunnel based on transverse galloping is proposed together with a method to optimize the energy extraction. In chapter 4 a methodology to predict the noise inside the train is described. Finally, some conclusions and the future work are summarized in chapter 5..

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(32) Chapter 2 Pressure waves in high speed railway tunnels. 2.1. Introduction. A well-known aerodynamic phenomenon in high speed trains is the propagation of the pressure waves generated when a train passes through a tunnel, which can give rise to several problems. The reflections of these waves at the discontinuities of the tunnel can meet the train several times inside the tunnel and can cause discomfort to the train passengers and also to the pedestrians near the tunnel entrance/exit due to the micro-pressure radiated outside from the tunnel portals. When a train approaches a tunnel entrance portal, the air inside the tunnel begins to be compressed due to the open-air local field preceding the train nose. Once the train head reaches the tunnel entrance, the pressure increases faster until the nose is completely inside the tunnel. This interaction between the tunnel entrance hood and the train nose determines the shape of the compression wave generated, but the total pressure gauge pN remains constant. The pressure continues to increase slowly due to the viscous effects on the tunnel wall and the train surface pf r , until the end of the train reaches the tunnel entrance portal, and a rarefaction wave is then generated with a pressure decrease pT . The pressure decreases suddenly pHP when the train nose passes the measurement point. These pressure variations are known as the train reference signature, and is defined in the standard EN1 [2006] (see Figure 2.1.1). When this pressure wave reaches the tunnel exit, part of the wave energy is radiated outside as a micro-pressure wave and part is reflected back inside the tunnel. At very low frequencies the exit radiates as a monopole source, and almost all the energy is reflected back. Discontinuities at the tunnel exit, like porosity or variations of the cross-section area, generate reflections which can increase the frequency of the signal and at the same time the capacity to radiate outside the tunnel. The micro-pressure radiated outside is proportional to the pressure gradient of the incident wave. In the literature, the effort to reduce the micro-pressure have been focused mainly on the optimization of the tunnel entrance and the nose shape of the train, reducing the pressure gradient. The efficiency of this option gets substantially reduced in long tunnels (more than 5 km) with small friction losses between the air and the interior walls, like in slab track tunnels, where. D. D D. D. 11.

(33) 12. CHAPTER 2. PRESSURE WAVES IN HIGH SPEED RAILWAY TUNNELS. Figure 2.1.1: Train reference signature defined by the standard EN14067-5:2006:E [2006].. the non-linear effects generate a steepening of the wave which progressively reduces the compression wave thickness, significantly increasing the pressure gradient and also the disturbance radiated from the tunnel portal. It becomes similar in strength to a sonic boom. A ballasted track is an effective porous sound absorbing material in the lowfrequency range, but the high maintenance costs in long tunnels make this option not feasible. One interesting goal would be to find a device with an attenuation capability as much as the ballast but with reduced maintenance costs. The design of railway tunnels for high speed train operation requires accurate models to study the wave propagation process and its interaction with the vehicle which implies long calculation times. However, this process can be somehow alleviated by using simplified models. The main advantage of simplified models is that the computational cost is quite low compared with more complex models. The most common simplified approach to deal with the interaction of pressure waves and vehicle is the use of models based on of the one-dimensional equations of gas dynamics. A method based on the propagation of the signature of the pressure waves inside the tunnel, which requires low CPU cost, is presented in William-Louis and Tournier [2005]. This method of characteristics, 1D finite difference, is used as a numerical scheme, only predicts pressure changes and is only valid for simple tunnels (without abrupt crosssection changes, air shafts, etc.), but allows to investigate trains crossings using different time delays in the entry time of the trains. In the zones where the flow is strongly three-dimensional (around tunnel portals, train ends) other methods have to be used. Concerning the interaction of the train head with the tunnel portal, in Iida et al. [2006] an analytical method based on the aeroacoustic theory developed by Howe is applied to a short “acoustically compact” hood having a window on its side wall. The boundary element method is used to calculate the potential flow through a portal of arbitrary geometry. A parametric analysis and an experimental study is performed in order to show the great influence in its performance of the relative length of the train nose to the distance between the window and the hood entrance. Another parametric numerical study of the micro-pressure wave is performed in Kaoua et al. [2006]. The results are validated with experimental data. Among the parameters considered are the train speed, train nose shape, tunnel length, track form, transitions in cross-section area at the portals, shafts distributed along the tunnel, and cross passages to an adjacent tunnel. The flow generated by a train in a tunnel with side branches is studied in WilliamLouis and Tournier [1998]. The results confirm that the use of shafts provides a very effective method to reduce pressure fluctuations in tunnels. The shafts divide the waves into secondary waves which can be more effectively damped by viscous dissipation or.