The tunnel-train-air interaction problem is investigated by using a numerical method able to provide relevant information about pressure fluctuations, aerodynamic drag characteristics and the “piston wind” effect. The method relies on a RNG k-ε two-equation turbulence model. It is shown that although reducing the oblique slope can alleviate the pressure gradient resulting from initial compression waves at the tunnel entrance, the pressure fluctuations in the tunnel are barely affected; however, a large reduction of micro-pressure wave amplitudes is found outside the tunnel. In comparison to the case where no tunnel hood is present, the amplitudes of micro-pressure waves at 40 m from the tunnel reach an acceptable range. The aerodynamic drag of the head and tail fluctuates greatly while that of the intermediate region undergoes only limited variations when the high-speed train passes through the double-hat oblique tunnel. It is shown that the effects of the oblique slope of the portal on the aerodynamic drag can almost be ignored while the train speed plays an important role.

High-speed railways usually employ straight lines, large curve radii, and small slopes such that bridges and tunnels account for a large proportion of the total length of the railway line in regions with vast expanses and mountainous areas [

With the increasing speed of high-speed trains passing through tunnels, the aerodynamic performance of tunnels is attracting greater attention. Problems such as micro-pressure wave, wake flow, and piston wind induced by a passing train not only pose threats to safe and stable train operation but also reduce passenger comfort. In many countries, these problems are usually alleviated by optimizing the opening rate of tunnel hoods [

All aforementioned studies suggest that appropriate settings of hat oblique portals at tunnel entrances can effectively alleviate the aerodynamic effects of tunnels. However, according to statistics on the construction of tunnel hoods at entrances, the mitigation effects on micro pressure waves gradually decrease as the length of the tunnel hood increases beyond a certain threshold. Furthermore, many commonly used measures (such as changing the streamline of the train head and setting hoods at tunnel entrances) have economic and commercial limitations [

This study aims to establish a three-dimensional numerical model for investigating micro-pressure waves at the exits of tunnels and aerodynamic drag fluctuations when high-speed trains pass through a double-hat oblique tunnel. The results can provide guidelines for designing high-speed railway tunnels.

The passing of a high-speed train through a tunnel can be regarded as a transient problem. The air in the tunnel is squeezed between the train surface and the tunnel wall; hence, it can be treated as a compressible ideal gas. The airflow around the train is strongly disturbed; in general, the Reynolds number is greater than 10^{6} and the flow field is in a turbulent state [

Mass conservation equation:

Energy conservation equation:

Momentum equation in the

Momentum equation in the

Momentum equation in the

Turbulent kinetic energy equation:

Turbulent dissipation equation:

At high Reynolds numbers, the turbulent viscosity (

where

The train and tunnel models are divided using a structured hexahedral mesh in ANSYS ICEM. The slip grid is used for the train and the surrounding air to realize relative movement between the train and the ground. The static and moving areas exchange flow field information through the interface. To accurately simulate the evolution of the flow field around the body when the train passes through the tunnel, the thickness of the first layer of the train surface is set to 0.001 m; the boundary layer is expanded by 30 layers at a ratio of 1.05, and it then increases at a higher rate. The mesh size in the forward direction of the train changes from 0.1 m to 1 m while the mesh size of the body is around 0.15 m. The overall number of elements for the mesh model is around 8.8 million, of which the number of elements for the double-hat oblique portal is around 50,000. The mesh distributions of the train surfaces, tunnel, and boundary layer are shown in

The meshed model is imported into ANSYS FLUENT CFD for calculation. The continuity and momentum equations are solved using a finite volume method [^{−3} s with 20 iterations in each time step, and the residual limit is 10^{−3}. Deng et al. pointed out that the results calculated by using this time step are consistent with the results obtained by Schober et al. using a 1:15 scale train model [

Parameters | Solution methods |
---|---|

Type | Density-based |

Time | Transient |

Formulation | Implicit |

Flux type | Roe FDS |

Gradient | Least-squares cell-based |

Flow/Turbulent kinetic energy/Turbulent dissipation rate | Second-order upwind |

Convection item/Viscosity item | Second-order central difference scheme |

Transient formulation | Second-order implicit |

The aerodynamic drag coefficient (

where

Two meshes with the same meshing strategy but different densities are constructed for mesh-independent analysis. The number of elements in the coarse mesh, which is the mesh model used in this study, is around 8.8 million. The fine mesh further refines the key areas, such as the train surface and the boundary layer; it contains more than 11.0 million elements.

As shown in

Compared with the model used in [

Carriage | Data in [ |
Data in this study | Error (%) |
---|---|---|---|

Head | 0.17 | 0.16 | 5.9 |

Middle | 0.13 | 0.14 | 7.7 |

Tail | 0.09 | 0.10 | 11.1 |

As can be seen from

Most of the compressed air flows forward together under the impetus of trains that pass through the tunnel at high speed [

As can be seen from

Further, As can also be seen from

The comparison of the gradient amplitude of the initial compression wave at a distance of 30 m from the entrance is shown in

Oblique slope | 1:1.00 | 1:1.75 | 1:2.00 |
---|---|---|---|

Maximum gradient coefficient of the initial compression wave | 3.71 | 3.24 | 3.04 |

Relative decline (%) | Reference | 12.7 | 18.1 |

The micro-pressure wave is a typical infrasonic wave phenomenon in the aerodynamic effects of high-speed railway tunnels, which is characterized by low frequencies and long wavelengths [

Oblique slope | 1:1.00 | 1:1.75 | 1:2.00 |
---|---|---|---|

The maximum coefficient of the micro-pressure wave | 0.0092 | 0.0086 | 0.0083 |

Relative decline (%) | Reference | 6.5 | 9.8 |

In [

The flow field on the train surface undergoes alternating positive and negative fluctuations owing to the repeated action of the pressure when the high-speed train is running in the tunnel, which leads to complex fluctuations in the aerodynamic drag [

This study investigated the pressure fluctuations and aerodynamic drag characteristics of a high-speed train passing through a double-hat oblique tunnel using the Reynolds method and the RNG

(1)The fluctuation of the piston wind induced by a passing train is complex and strong, while the wake flow always exists and the intensity change is not obvious.

(2)The reduction of the oblique slope has a significant mitigation effect on the gradient of the initial compression waves when a train passes through a tunnel, and the maximum decrease is around 18.1%.

(3)Compared with tunnels without hoods, the amplitude of the micro-pressure wave at 40 m from the tunnel exit is within an acceptable range when the double-hat oblique portal is set at the tunnel ports. The smaller the oblique slope, the more significant is the mitigation effect on the micro pressure wave outside the tunnel exit.

(4)The drag of the train head and tail fluctuates severely when the train passes through the tunnel, while the fluctuation of the intermediate train is gentle. The decrease in the oblique slope of the portal does not have significant effects on the train drag. However, the aerodynamic drag increases with the train speed.

The authors thank TopEdit (