Hello Viper488,
I have some experience that you may find interesting:
1. In the '80s, I was involved in altitude chamber testing of an aircraft engine that was turbo normalized. We achieved a test point with 30"HgAbs intake manifold pressure and 18"HgAbs pre-turbo system pressure (the turbo system was a two-stage system). The high positive delta P across the engine helped achieve a BSFC of 0.36 lb/bhp-hr, which is relatively good economy for a spark ignition avgas engine. However, the engine/turbo system was designed for one operating point, and transient response was not good. There is a lesson, though. Consider the whole four stroke cycle and the integrated PdV for the whole cycle when modeling the indicated work.
2. A little later, I was involved with the application of a VNT turbo to a passenger car engine. We were testing in the lab with a simulated exhaust restriction when we ran into a problem and had to remove the exhaust restriction. Engine bhp rose from 175 to 225 (with the same intake MAP and fuel flow) when we ran without the production (cat and muffler) restriction level. Some production exhaust systems can be very restrictive.
3. If you look at the turbo installation in large stationary engines, you will note exhaust diffusers that diffuse the turbine exit velocity prior to an atmospheric dump. This is done to reduce the turbine out static pressure, because it has a significant effect on engine system efficiency.
The bottom line is that careful turbocharger exhaust design can improve overall system power output amd thermal efficiency. However, this is rarely done in passenger cars (including performance automobiles) for two reasons:
1. exhaust diffusion requires space and can be bulky
2. transient response demands usually require the turbine expander to be undersized for most of the engine operating points and a lot of entropy is generated by the mass bypass control (wastegate) anyway, so why bother perfecting the exhaust?
I hope this wasn't too wordy.
PS. The many comments regarding turbine work are good but not quite complete. Turbine work is related to the mass flow times the actual enthalpy change across the stage. So it is related to mass flow, available pressure ratio, inlet temperature, gas composition, and turbine efficiency. The turbine expander work conditions are easy to quantitatively understand in a steady-state test rig, but can be more complicated in the dynamic environment of a recip engine exhaust stream.
