Isentropic Turbine Specific Work
Isentropic Turbine Specific Work
The turbine stage in a gas turbine or jet engine extracts work by expanding hot combustion gas down to a lower pressure, and the isentropic (ideal, loss-free) specific work sets the theoretical ceiling on how much shaft work that expansion can deliver per unit mass of gas — mirroring the compressor work calculation but in reverse, since here temperature drops as pressure drops. Because the turbine in a gas turbine must supply enough work to drive the compressor before any is left over as useful output, accurately estimating turbine specific work is essential to predicting whether a given cycle design produces meaningful net power at all.
The isentropic turbine work is w = cp·T3·(1 - (1/rp)^((k-1)/k)), per unit mass of gas expanded. where cp is the gas's specific heat at constant pressure, T3 is the turbine inlet temperature, rp is the expansion pressure ratio, and k is the ratio of specific heats.
Inputs
cp_gas := 1.148 kJ/(kg·K)=1148 m^2/K/s^2
T_3 := 1400 K=1400 K
r_p3 := 6=6
k_gas2 := 1.33=1.33
The bracketed term gives the fractional temperature drop an ideal isentropic expansion produces across this pressure ratio; scaling it by cp and the inlet temperature converts that temperature drop into the specific shaft work the turbine ideally delivers.
w_turb := cp_gas·T_3·(1 - (1/r_p3)^((k_gas2-1)/k_gas2))=576826.21 m^2/s^2
Results
The result, on the order of 500–600 kJ/kg, is a realistic ideal turbine specific work for a gas turbine hot section at these conditions, and comparing it against the compressor specific work computed separately shows how much net work per unit mass is left over to drive a generator. In a real gas turbine some of this turbine work also has to cover cooling-air bleed and mechanical losses, and an isentropic efficiency (typically 0.85–0.92) reduces actual work below this ideal figure. Raising turbine inlet temperature T3 is the single most effective way to increase both this specific work and cycle efficiency, which is why turbine inlet temperature is the headline spec pushed by every generation of gas turbine technology.
Assumptions & limitations
- Isentropic (reversible, adiabatic) expansion assumed — no losses.
- Ideal gas with constant specific heats over the expansion.
- Does not subtract compressor work or cooling-air penalties.
- Single-stage expansion; multistage reheat would change the result.