Influence of flow rate on pressure ratio in turbocharger

Garrettmotion

A turbocharger consists of a compressor wheel (intake) and turbine wheel (exhaust) connected by a shaft. Turbocharger boosts the intake air pressure of an internal combustion engine in order to create more horsepower at high-rpm region. The exhaust turbine extracts rotational energy from the flow of exhaust gas and meanwhile the compressor wheel rotates. Seals prevent oil leakage between the compressor and turbine. Turbocharger usually struggles to boost horsepower at low-rpm range because the flow rate of exhaust gas is low when the crankshaft rotates slowly. The Aspect Ratio (AR) is the ratio of the area of the exhaust turbine inlet to the radius from the turbine impeller center. A large AR increases the spool up time (more turbo lag) but produces more horsepower at high-rpm range.
  

dieseinlet

To select a right turbocharger, two important parameters (i.e. pressure-ratio and flow rate) are required to consider carefully. Assume you want to boost the Chevy 302 engine to 650HP with the help of a turbocharger, you are recommended to go through the following calculation before you buy a turbocharger.

Flow rate FR = HP x AF x BSFC

where HP is the desired horsepower at flywheel, AF is air-fuel ratio and BSFC is brake specific fuel consumption per minute

Based on this equation, the expected flow rate = 650 x 12.4 x (0.38/60) = 51.1 lb/min

Next you need to determine the manifold pressure (MP)

MP =  FR x R x (460 + T) / V_eff / (0.5 x w) / V

where FR is the expected flow rate in lb/min, R ~ 630 is gas constant, T is temperature in F, V_eff is volumetric efficiency, w is the desired RPM and V is the total engine displacement in cc.

Substitute all the parameters into this equation,

Manifold pressure = 51 x 639.6 x (460 + 130) / 0.87 / (0.5 x 7000) / 301.44 = 20.9 psi

To encounter the energy loss between compressor and manifold region, it is usually accurate if you add 1-4 psi to the manifold pressure empirically. Now the corrected manifold pressure becomes 20.9 + 2 = 22.9 psi.

The inlet pressure of the compressor at sea level is 14.7 psi. To take into account the energy loss, the corrected inlet pressure of compressor is 14.7 - 1 =13.7 psi empirically

Now you can estimate the pressure-ratio (PR) easily. i.e. 22.9 / 13.7 = 1.67

Then you should search for a turbocharger that locates the pressure-ratio and flow rate correctly in the compressor map. The turbocharger (Garrett-GT4049R-94-52) is a good option arguably. Why? Because the data point at peak performance (FR,PR) = (51.1, 1.67) is not located in the 'surge' or 'choke' region.

'Surge': Turbocharger rotates too slow (grey area)
'Choke': Turbocharger rotates too fast (pink area)
Red line: The rotational speed (RPM) of the common shaft
Black dot: Measurement 

Compressor map 

To optimize the performance of turbocharger, you need to install a wastegate. When the incoming pressure is larger than the threshold pressure of the wastegate, the valve in the wastegate will be opened. If the wastegate is easy to open, less burnt-out gas will pass through the exhaust pipe. This weakens the turbo performance because the torque on the turbine is decreased. However, the turbo will be damaged if the wastegate does not exist.

Simplified diagram produced by Thomas Schwenke

Here I tune the spring constant in order to adjust the wastegate pressure. Setting the wastegate pressure at 10 psi in the Garrett turbocharger can push the Chevy engine to 623 HP. This is pretty close to my target (650HP)

Measurement data

Intercooler is another device to influence the effect of turbocharger. While the wheel of the compressor rotates very rapidly, it heats up the intake gas. The aim of an intercooler is to cool down the intake gas that increases the density of air in the manifold. The reduction in air temperature across the intercooler is measured by the drop of pressure. The intercooler operating at the maximum and minimum conditions decrease the air pressure by 3 psi and 0.4 psi, respectively. This affects the dyno data remarkably. The effect of the intercooler on turbocharger starts to pale in the high-rpm region because the cooling power is limited.