Turbocharger selection is made from the manufacturer's compressor and turbine maps. Those maps are measured on a test rig under steady flow conditions.
In a real engine the flow reaching the turbine is not steady: a pressure pulse arrives at each exhaust valve opening. Through the cycle the turbine wanders across different points of the map, and the cycle average differs from what a single point on the map gives.
The difference is marked in small engines and at low speed in particular.
Turbo lag is an inertia problem
When the throttle is opened the turbine does not accelerate immediately: the rotor's moment of inertia waits for the exhaust energy to build. The lag is directly proportional to rotor inertia — small, light rotors respond quickly but limit capacity at high speed.
This is a classic trade-off, and the job of the analysis is to measure it.
Do not overlook the thermal side
The turbine housing runs at exhaust temperature and the compressor housing relatively cool; both are attached to the same centre housing. The bearing region sits between them and the oil temperature is a critical criterion — overheating cokes the oil and ends the bearing's life.
This is a conjugate problem: the gas side, the metal and the oil circuit must be solved together. When the engine stops the cooling stops too, and the temperature briefly rises (heat soak); that transient has to be examined separately. See the steady versus transient note.
Modelling
The surge limit on the compressor side. See the surge note.
Pulsating flow on the turbine side. A steady analysis reproduces the map; cycle behaviour requires transient boundary conditions.
Volute geometry. Both the turbine and compressor volutes break circumferential uniformity; a single-passage periodic model cannot see that effect.
References
- Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149
- Shah, R. K. & Sekulić, D. P. (2003). Fundamentals of Heat Exchanger Design. John Wiley & Sons. DOI: 10.1002/9780470172605