Question

A turbo charger boosts the inlet air pressure to an automobile engine. It consists of an exhaust gas driven turbine directly connected to an air compressor,  For a certain engine load the conditions are given in the figure. Assume that both the turbine and the compressor are reversible and adiabatic having also the same mass flow rate. Calculate the turbine exit temperature and power output. Find also the compressor exit pressure and temperature.

Answer 1

CV: Turbine, Steady single inlet and exit flows,

Process: adiabatic: q = 0,

reversible: s_gen = 0

EnergyEq : w_T = h₃ − h₄ ,

Entropy Eq.  s₄ = s₃

The property relation for ideal gas , k from

C.V. Compressor, steady 1 inlet and 1 exit, same flow rate as turbine.

Energy Eq. -w_C = h₂ − h₁ ,

Entropy Eq.  s₂ = s₁

Express the energy equation for the shaft and compressor having the turbine power as input with the same mass flow rate so we get

-w_C = w_T = 130.5 = C_P0(T₂ - T₁) = 1.004(T₂ - 303.2) T₂ = 433.2 K

The property relation for s₂ = s₁ is and inverted as