2.5 · Compare regeneration, intercooling, and reheat in gas turbines

University of Alberta MEC E 340: Applied Thermodynamics

Gas Power Cycles

How heat recovery and staged compression or expansion affect work and heat input

What you will learn

• Describe where regeneration, intercooling, and reheat occur in a gas-turbine cycle.
• Use simple energy balances to estimate effects on work or external heat transfer.
• Compare the modifications without assuming that more turbine work means higher cycle efficiency.

1. Set up the comparison: states, signs, and balances

• Compare net cycle work and external heat input, not just turbine work.
• State what is held constant before comparing cases.

2. Regeneration: reuse turbine-exhaust heat

• Main effect: lower external heat input for the same turbine-inlet state.
• Check the inlet temperatures before claiming that heat can flow in the desired direction.

3. Intercooling and reheat: change compression and expansion

• Intercooling: heat leaves the working fluid between compressor stages.
• Reheat: heat enters the working fluid between turbine stages.
• Regeneration: exhaust heat is transferred to compressed air.

4. A practical comparison method

• Use consistent assumptions and comparison conditions.
• Check energy-transfer directions and distinguish component work from cycle performance.

Worked example

Estimate heat saved by regeneration

1. Find the compressed-air outlet temperature
   Effectiveness is the actual cold-stream temperature rise divided by its maximum possible rise based on the inlet temperatures. Use the supplied effectiveness and inlet temperatures.
   $$T_{2R}=500+0.75(700-500)=650\ \mathrm{K}$$
2. Compare external heat inputs
   With regeneration, external heating raises the air from 650 K to 1100 K. Without regeneration, it raises the air from 500 K to 1100 K. Their difference is the heat saved per kilogram under the stated constant-specific-heat assumption. \Delta q_{in}=1.005[(1100-500)-(1100-650)]=150.75\ $\mathrm{kJ/kg}$

Worked example

Estimate compressor-work reduction with intercooling

1. Estimate the one-stage outlet temperature
   For the stated ideal-gas, isentropic compression model, the temperature ratio is the pressure ratio raised to $(\gamma-1)/\gamma$. Apply the full pressure ratio.
   $$T_{out}=300(16)^{2/7}\approx662.4\ \mathrm{K}$$
2. Estimate work with two stages
   Each stage has pressure ratio 4. Perfect intercooling returns the air to 300 K before the second stage, so both stages have the same temperature rise. Sum their enthalpy increases.
   $$w_2=2(1.005)[300(4^{2/7}-1)]\approx293.1\ \mathrm{kJ/kg}$$
3. Compare the work estimates
   The one-stage work is the enthalpy increase from 300 K to the one-stage outlet temperature. Subtract the two-stage work to find the reduction.
   $$w_1=1.005(662.4-300)\approx364.2\ \mathrm{kJ/kg};\quad w_1-w_2\approx71.1\ \mathrm{kJ/kg}$$

Worked example

Estimate the effect of reheat on turbine work

1. Calculate the single-expansion outlet temperature and work
   Use the ideal-gas isentropic temperature relation with the full pressure ratio. Turbine work per kilogram is the enthalpy decrease under these assumptions.
   $$T_{out,1}=1200(16^{-2/7})\approx543.6\ \mathrm{K};\quad w_{t,1}=1.005(1200-543.6)\approx659.9\ \mathrm{kJ/kg}$$
2. Calculate work from both reheated stages
   Each stage has pressure ratio 4. The first stage begins at 1200 K, and reheating returns the second-stage inlet to 1200 K. Both ideal stages therefore have the same temperature drop.
   $$T_{out,stage}=1200(4^{-2/7})\approx807.6\ \mathrm{K};\quad w_{t,2}=2(1.005)(1200-807.6)\approx789.0\ \mathrm{kJ/kg}$$
3. Compare turbine work
   Subtract single-expansion work from work with reheat. This measures the turbine-work increase only; reheat also requires external heat, so this calculation does not determine cycle efficiency.
   $$w_{t,2}-w_{t,1}\approx129.1\ \mathrm{kJ/kg}$$

Common mistakes and how to avoid them

Lesson summary

• Regeneration recovers turbine-exhaust heat to reduce external heat input.
• Intercooling removes heat between compressor stages and can reduce compressor work under stated conditions.
• Reheat adds heat between turbine stages and can increase turbine work, but also increases external heat supplied.
• A cycle-efficiency comparison requires net work and total external heat input on a consistent basis.

Check your understanding

Key terms

Regeneration

Heat recovery from turbine exhaust to preheat compressed working fluid before external heating.

Intercooling

Heat removal from the working fluid between compressor stages.

Reheat

Heat addition to the working fluid between turbine expansion stages.

Thermal efficiency

The ratio of cycle net work output to external heat input.

Continue through MEC E 340

View the complete MEC E 340 University of Alberta MEC E 340: Applied Thermodynamics curriculum and lessons

• 2.1 · State air-standard and cold-air-standard assumptions
• 1.1 · Define the system, working fluid, state, and process
• 1.2 · Read property tables and identify phase regions
• 1.3 · Apply steady-flow mass and energy balances to cycle devices
• 1.4 · Interpret schematic P–v and T–s process diagrams
• 3.2 · Account for turbine and pump isentropic efficiencies

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