Exhaust gas turbocharger for an internal combustion engine

1. 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 (b min ) in the back-pressure position in order to secure a flow path in the direction of the turbine rotor, wherein the minimum distance (b min ) between two adjacent guide vanes in the back-pressure position is

  b min ≦0.5 D TR /z,

where

D TR 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.

2. The exhaust gas turbocharger according to claim 1 , wherein the minimum distance apart (b min ) between two adjacent guide vanes obeys the relationship

b min ≦0.3 D TR /z.

3. The exhaust gas turbocharger according to claim 1 , wherein sections of each two adjacent guide vanes overlap in the peripheral direction of the guide cascade, at least in the back-pressure position.

4. The exhaust gas turbocharger according to claim 1 , wherein a radially inner trailing edge of a guide vane has a trailing edge thickness which is at least 0.2 times the minimum distance between adjacent guide vanes.

5. The exhaust gas turbocharger according to claim 1 , wherein twice a distance (D HK ) between the supercharger center line and the trailing edge of a guide vane obeys the relationship

 D HK ≦1.1D TR

with respect to the diameter (D TR ) of the turbine rotor.

6. The exhaust gas turbocharger according to claim 5 , wherein twice the distance apart (D HK ) between the supercharger center line and the trailing edge of a guide vane obeys the relationship

D HK ≦1.05D TR

with respect to the diameter (D TR ) of the turbine rotor.

7. The exhaust gas turbocharger according to claim 1 , wherein the guide vanes are immovably connected to the guide cascade and the guide cascade is moved axially into the inlet flow cross section, the position in which the guide cascade is moved into the inlet flow cross section corresponding to the back-pressure position and the position in which the guide cascade is moved out of the inlet flow cross section corresponding to the open position.

8. The exhaust gas turbocharger according to claim 1 , wherein the guide vanes are coupled to the guide cascade so that the guide vanes rotate and have to be adjusted between the back-pressure position and the open position.

9. The exhaust gas turbocharger according to claim 1 , wherein a total of nine guide vanes, which are distributed over the periphery of the guide cascade, are provided.