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A single-stage turbocharger turbine is developed with the objective of enabling a gasoline spark-ignition engine to operate under lean-burn conditions with an air-to-fuel ratio of λ=2 in the range of the Worldwide Harmonized Light-Duty Vehicles Test Cycle. For this purpose, extensive 1-D engine simulations are performed using a combination of a simple compressor and simple turbine model as well as a combination of the stock compressor and a simple turbine model. The results show that an isentropic turbine efficiency of more than 70% over a wide operating range is required for the desired engine operation - especially with regard to the low-end-torque. Based on the crank-angle-resolved engine simulation data, turbine requirements are determined. Their evaluation shows that an axial turbine is a reasonable alternative to conventional radial turbines for this application. Next, a preliminary axial turbine is designed using 1-D/2-D design approaches.