Turbocharger turbine to compressor sizing

[Ibrahim M]

Hello,
What is the theory behind sizing of turbine wheel to compressor wheel ?

I take that compressor inducer to turbine exducer is what matters the most ?

But why did we see "hybrid" turbos appear ? Like a t4 compressor with a t3 turbine ?

 

[Lou Scannon]

They are a compromise, using what is available off the shelf. Well, not exactly, as Garrett designed a couple of T3/T4 hybrids for GM back in the 80s, but in both cases, the turbine was a dedicated design for the respective applications.
The turbine should be designed to work well with a dedicated range of compressor characteristics.
The diameter ratio of the turbine inducer to compressor exducer is a compromise, but should be in the range 10-15% smaller for typical layouts. Making the turbine smaller helps with inertia, but negatively impacts turbine efficiency due to the effect of the tip speed ratio. This effect arises from the angle at which the gas is meeting the moving blade departing significantly from the design point.