METHODS FOR IMPROVEMENT OF THERMAL EFFICIENCY OF OPEN CYCLE CONSTANT PRESSURE GAS TURBINE

The thermal efficiency of open cycle constant pressure gas turbine can be improved by the following methods:

1. Regeneration
2. Intercooling
3. Reheating
4. Combination of above

1 Regeneration

In this method, the heat of the exhaust gases is used to heat the air coming out from the compressor, thus reducing the mass of fuel supplied in the combustion chamber. A schematic diagram of such a plant is shown in Fig. 16.9 (a).

1. Without Machine EfficienciesThe T-s diagram without machine efficiencies is shown in Fig. 16.9 (b).For 1 kg of airCompressor work,   w_c = w_1 − 2 = c_p (T₂ − T₁)Heat supplied,    q_s = q_5 − 3 = c_p (T₃ − T₅)Turbine work,    w_t =w_3 − 4 =c_p (T₃ − T₄)Net work,     w_net = w_t – w_c = c_p (T₃ – T₄) – c_p (T₂ – T₁)Figure 16.9 Open cycle gas turbine with regeneration: (a) Schematic diagram, (b) T-s diagram without machine efficiencies, (c) T-s diagram with machine efficienciesThermal efficiency, In an ideal regenerator, T₄ = T₅    Figure 16.10 Variation of thermal efficiency with pressure ratio for open cycle gas turbine with regenerationThe variation of thermal efficiency with pressure ratio is shown in Fig. 16.10. It may be seen that thermal efficiency increases with an increase in  and decreases with increase in r_p.
2. Considering Machine EfficienciesThe T-s diagram is shown in Fig. 16.9 (c).    Figure 16.11 Actual regeneration process  
3. Effectiveness of RegeneratorIn actual practice, the rise in temperature from T_2′ to T₅ = T_4′ is not possible. The actual temperature of air will be T_5′ < T₅. Hence, actual thermal efficiency [see Fig. (16.11)] of the cycle becomes,The effectiveness of the regeneration is given by where ṁ_a, ṁ_g = mass rate of flow of air and exhaust gases, respectivelyc_pa, c_pg = specific heats of air and exhaust gases, respectively.

2 Intercooling

The work consumed by the compressor can be reduced by compressing the air in two stages and incorporating the intercooler in between, as shown in Fig. 16.12 (a). The corresponding T-s diagram is shown in Fig. 16.12 (b).

Figure 16.12 Gas turbine plant with intercooling: (a) Schematic diagram, (b) T-s diagram

For perfect cooling, T₃ = T₁ and if n_c1 = n_c2 = n_c′ then

w_net = wt – w_c = c_p (T₅ – T_6′) – [c_p (T_2′ – T₁) + c_p (T_4′ – T₃)]

For perfect intercooling,T₃ = T₁ and if h_c1 = η_c2 = η_c, then

3 Reheating

A considerable increase in power output can be achieved by expanding the gases in two stages with a reheat combustion chamber between the two as shown in Fig. 16.13 (a). The corresponding T-s diagram is shown in Fig. 16.13 (b).

w_t = c_pg (T₃ – T₄′) + c_pg (T₅ – T₆′)

= c_pg η_t1 (T₃ – T₄) + c_pg η_t2 (T₅ – T₆)

where 

Let 

Figure 16.13 Gas turbine plant with reheating: (a) Schematic diagram, (b) T-s diagram

If η_t1 = η_t2 = η_t and T₅ = T₃, then

4 Reheat and Regenerative Cycle

This cycle is shown in Fig. 16.14.

w_c = c_p (T₂ – T₁)

q_s = q_{7 – 3} + q_{4 – 5} = c_p (T₃ – T₇) + c_p (T₅ – T₄)

w_t = w_{3 – 4} + w_{5 – 6} = c_p (T₃ – T₄) + c_p (T₅ – T₆)

Figure 16.14 Gas turbine plant with reheat and regeneration: (a) Schematic diagram, (b) T-s diagram

Net work w_net = w_t – w_c

= c_p [(T₃ – T₄) + (T₅ – T₆) – (T₂ – T₁)]

Let  so that r_p = r₁r₂

So that c = c₁c₂

Now, 

Now, T₇ = T₄ and T₅ = T₃

5 Cycle with Intercooling and Regeneration

The schematic arrangement and T-s diagram of the cycle are shown in Fig. 16.15.

w_c = w_{1 – 2} + w_{3 – 4} = c_p [(T₂ – T₁) + (T₄ – T₃)]

q_s = q_{7 – 5} = c_p (T₅ – T₇)

w_t = w_{5 – 6} = c_p (T₅ – T₆)

w_net=w_t – w_c = c_p [(T₅ – T₆) – (T₂ – T₁) – (T₄ – T₃)]

Let  so that c = c₁c₂ and T₃ = T₁

Figure 16.15 Gas turbine plant with inter cooler and regeneration: (a) Schematic diagram, (b) T-s diagram

Now, q_s = c_p (T₅ – T₇)

6 Cycle with Intercooling and Reheating

The schematic arrangement of this cycle is shown in Fig. 16.16 (a) and the corresponding T-s diagram in Fig. 16.16 (b).

w_c = c_p [(T₂ – T₁) + (T₄ – T₃)]

q_s = c_p [(T₅ – T₄) + (T₇ – T₆)]

w_t = c_p [(T₅ – T₆) + (T₇ – T₈)]

w_net = w_t – w_c = c_p [(T₅ – T₆) + (T₇ – T₈) – (T₂ – T₁) – (T₄ − T₃)]

Now, T₃ = T₁ and T₇ = T₅ for perfect intercooling and reheating, respectively. Then,

Thus, c = c₁c₂

For maximum work output, 

or 

Figure 16.16 Gas turbine cycle with intercooler and reheating: (a) Schematic diagram, (b) T-s diagram

7 Cycle with Intercooling, Regeneration and Reheating

The schematic arrangement of the cycle and corresponding T-s diagram are shown Fig. 16.17.

w_c = c_p [(T₂ − T₁) + (T₄ − T₃)]

q_s = c_p [(T₅ − T₉) + (T₇ − T₆)]

w_t = c_p [(T₅ − T₆) + (T₇ − T₈)]

w_net = w_t − w_c = c_p [(T₅ − T₆ + T₇ − T₈) − (T₂ − T₁ + T₄ − T₃)]

T₇ = T₅

Let T₁=T₃ and T₅=T₇ so that c₁=c₂