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ENGR5003 / Week 5
Lecture 13 worked example 2 - ideal Brayton cycle with air tablesTutorialCurrent spec2:215 min

ENGR5003 Lecture 13 worked example 2 (slides 11-14)

A gas-turbine power plant operating on an ideal Brayton cycle (Figure 1) has a pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 1300 K at the turbine inlet. Calculate the gas temperatures at the exits of the compressor and the turbine. Also calculate the back work ratio, the cycle work and the thermal efficiency.

Use the ideal-gas air table (Cengel Table A-17), where PrP_r is the relative pressure, with Pr2/Pr1=p2/p1P_{r2}/P_{r1} = p_2/p_1 for an isentropic process:

T (K)h (kJ/kg)PrP_r
300300.191.386
540544.3511.10
760778.1839.27
780800.0343.35
13001395.95330.9

Then repeat with the cold-air-standard assumptions (γ=1.4\gamma = 1.4, cp=1.005 kJ/(kg K)c_p = 1.005\ \mathrm{kJ/(kg\,K)}) and compare.

Figure 1: ideal Brayton cycle on a T-s diagram (1-2 compressor, 2-3 heat addition at p2, 3-4 turbine, 4-1 heat rejection at p1).
Figure 1: ideal Brayton cycle on a T-s diagram (1-2 compressor, 2-3 heat addition at p2, 3-4 turbine, 4-1 heat rejection at p1).
Formulas you may need
  • SFEE, adiabatic, negligible KE and PE: w=Δhw = \Delta h (on the formula sheet)
  • Isentropic relation with relative pressure: Pr2Pr1=p2p1\dfrac{P_{r2}}{P_{r1}} = \dfrac{p_2}{p_1} (learn this, Lecture 13; tables provided)
  • Back work ratio rbw=win/woutr_{bw} = w_{in}/w_{out}, wnet=wout(1−rbw)w_{net} = w_{out}(1 - r_{bw}) (on the formula sheet)
  • Brayton efficiency (constant cpc_p): η=1−rp−(γ−1)/γ\eta = 1 - r_p^{-(\gamma-1)/\gamma} (on the formula sheet)
  • Linear interpolation (learn this)
  1. (a)
    Temperatures at the compressor and turbine exits (air tables).
  2. (b)
    Back work ratio, net (cycle) work and thermal efficiency (air tables).
  3. (c)
    The same quantities with constant specific heats (cold-air standard).