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.