Exhaust gas turbocharger for an internal combustion engine

An exhaust gas turbocharger for an internal combustion engine, having an exhaust gas turbine, which is arranged in the exhaust system of the internal combustion engine, and a compressor, which is arranged in the induction system and is connected to the exhaust gas turbine by means of a shaft, having variable turbine geometry associated with the exhaust gas turbine for adjustably setting a radial flow inlet cross section to the turbine rotor between a back-pressure position which reduces the inlet flow cross section and an open position which increases the inlet flow cross section, the variable turbine geometry being configured as a guide cascade, which encompasses the turbine rotor and has guide vanes distributed around the periphery, and adjacent guide vanes having a minimum distance apart (bmin) in the back-pressure position in order to secure a flow path in the direction of the turbine rotor, wherein the minimum distance (bmin) between two adjacent guide vanes in the back-pressure position is

• bmin≦0.5DTR/z,
• where
• DTR designates the diameter of the turbine rotor,
• z designates the number of guide vanes of the guide cascade,
• and in that there is a flow edge on the radially inner surface of each guide vane—on the surface facing towards the adjacent guide vane—the flow edge including an angle (α), which obeys the relationship
• α
• =
• k
• ⁢
• ⁢
• arctan
• ⁡
• (
• 1
• k
• ⁢
• M
• 2
• -
• 1
• )
• -
• arctan
• ⁡
• (
• M
• 2
• -
• 1
• )
• ,
• k
• =
• κ
• +
• 1
• κ
• -
• 1
• where
• M designates an average Mach number in the region of the guide vane trailing edge,
• κ designates the isentropic exponent.