In variable nozzle geometry turbines (VNT), the vanes that form the nozzle are opened to control turbine mass flow and expansion ratio (ER) in order to allow better engine matching and the generation of more turbine power. In application to turbocharged road vehicles, the vanes are closed to provide higher boost pressure for engine and vehicle acceleration, and may also be used for engine braking assistance. In both situations, high nozzle expansion ratios (ERs) are created, and shockwaves may be produced from the nozzles. These shocks reduce turbine efficiency and can cause high cycle fatigue (HCF) damage to the downstream rotor blades. Design of high ER radial nozzles is difficult for VNT because transonic flows are very sensitive to small changes to vane geometry, and there is a large semi-vaneless space after the nozzle throat. Shock minimised nozzle designs are therefore often accomplished by an auto-optimisation technique. While design targets may be achieved, this technique does not offer sufficient insight into how and why an optimal flow field has been derived, so the same optimisation procedure must be applied to every new design. In this paper, a new design method that overcomes this problem is proposed. The method first uses a conformal mapping to transfer a radial nozzle from the r-0 plane into the x-y plane. The mapped nozzle displays amplification of supersonic acceleration that is explained by the curvature changes brought about by the mapping. In addition, a link between shock strength and the flatness of the suction surface of the mapped nozzle was found. These features can be utilised to design nozzles with reduced shock loss. Nozzles for 6:1 ER were designed in this way and CFD results show significantly weaker nozzle shockwaves. Other performances of the nozzles are either improved or unaffected.

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