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Qwestrum Engineering360 · Mechanical Engineering · Applied Thermodynamics

Gas Turbine Cycles

The Brayton cycle efficiency is η = 1 − 1/r_p^((γ−1)/γ), depending on the pressure ratio r_p. Net work is turbine minus compressor work; the high back-work ratio distinguishes gas turbines, per P.K. Nag.
Exam tip: lock the sign convention (Q into system, W by system in P.K. Nag) before substituting; use absolute temperature for ideal-gas and efficiency ratios.

Key formulas & points

Skim these first — then read the full notes below.

  • Open cycle: combustion replaces heat addition at constant P
  • Intercooling reduces compressor work; reheating increases turbine work
  • Back work ratio high (~40–50%) for gas turbines

Topic details

Introduction

The Brayton (Joule) cycle underlies gas turbines and jet engines and is examined alongside the steam cycle. P.K. Nag models it as two isentropics (compressor, turbine) and two constant-pressure processes (combustor, exhaust/cooler).

Scope in B.Tech and GATE syllabus

Efficiency rises with pressure ratio, but net work peaks at an optimum pressure ratio r_p,opt = (T_max/T_min)^(γ/2(γ−1)) because compressor work eventually eats into turbine output. The back-work ratio (compressor/turbine work) is large (~40–50 %), unlike steam cycles.

Why this topic matters in practice

Intercooling reduces compressor work, reheating increases turbine work, and regeneration recovers exhaust heat — the three improvements. Recognising the optimum pressure ratio and correctly computing both compressor and turbine work through isentropic relations are the exam essentials.

Key relations & formulas

ηBrayton=1−1rp((γ−1)γ)\eta_{Brayton} = 1 - \frac{1}{r_{p}}^(\frac{(\gamma-1)}{\gamma})
(r_p = P₂/P₁, pressure ratio)
Wnet=Wturb−WcompW_{net} = W_{turb} - W_{comp}
(net work per kg air)
rp,opt=(TmaxTmin)(γ/(2(γ−1)))r_{p},opt = (\frac{T_{max}}{T_{min}})^(\gamma/(2(\gamma-1)))
(optimum pressure ratio)
ηregen=1−(T1T3)(rp((γ−1)γ)−1)\eta_{regen} = 1 - (\frac{T_{1}}{T_{3}})(r_{p}^(\frac{(\gamma-1)}{\gamma}) - 1)
(with regeneration)

Notation and sign conventions

Relation 1 —
\eta_{Brayton} = 1 - \frac{1}{r_{p}}^
ηBrayton=1−1rp((γ−1)γ)\eta_{Brayton} = 1 - \frac{1}{r_{p}}^(\frac{(\gamma-1)}{\gamma})
(r_p = P₂/P₁, pressure ratio)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Wnet=Wturb−WcompW_{net} = W_{turb} - W_{comp}
Wnet=Wturb−WcompW_{net} = W_{turb} - W_{comp}
(net work per kg air)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
rp,opt=r_{p},opt =
rp,opt=(TmaxTmin)(γ/(2(γ−1)))r_{p},opt = (\frac{T_{max}}{T_{min}})^(\gamma/(2(\gamma-1)))
(optimum pressure ratio)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
ηregen=1−\eta_{regen} = 1 -
ηregen=1−(T1T3)(rp((γ−1)γ)−1)\eta_{regen} = 1 - (\frac{T_{1}}{T_{3}})(r_{p}^(\frac{(\gamma-1)}{\gamma}) - 1)
(with regeneration)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

The Brayton cycle compresses air isentropically (1→2), heats it at constant pressure (2→3), expands it isentropically through the turbine (3→4), and rejects heat at constant pressure (4→1). Efficiency depends only on pressure ratio: η = 1 − 1/r_p^((γ−1)/γ).

Governing relations in practice

Both compressor and turbine work use isentropic temperature relations T₂/T₁ = r_p^((γ−1)/γ). Net work w_net = c_p(T₃ − T₄) − c_p(T₂ − T₁); the back-work ratio w_comp/w_turb is high because compressing a gas is costly.

Design and analysis considerations

Net work per unit mass is maximised at r_p,opt = (T_max/T_min)^(γ/2(γ−1)), a key optimisation result. Beyond it, added pressure ratio raises efficiency but reduces net work and increases size.

Advanced theory and extensions

Regeneration transfers turbine-exhaust heat to compressed air before combustion, useful when T₄ > T₂; intercooling and reheating with regeneration approach the Ericsson-cycle efficiency. These modifications make industrial gas turbines competitive despite the high back-work ratio.

Assumptions and validity limits

State assumptions explicitly before using any relation for gas turbine cycles — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Applied Thermodynamics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Applied Thermodynamics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to gas turbine cycles.
4. Use equation 1:
\eta_{Brayton} = 1 - \frac{1}{r_{p}}^
.
5. Use equation 2:
Wnet=Wturb−WcompW_{net} = W_{turb} - W_{comp}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Gas Turbine Cycles appears in IC engines, gas turbines, and compressors. In Indian mechanical curricula this topic is tested because it connects theory to air-standard and vapour power cycles.
GATE and semester exams often combine gas turbine cycles with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use gas turbine cycles?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Ignoring compressor work and equating net work to turbine work (back-work ratio is large)
• Using compression-ratio (volume) instead of pressure-ratio in the Brayton formula
• Applying regeneration when T₄ < T₂ (heat would flow the wrong way)
• Confusing the optimum pressure ratio for maximum work with that for maximum efficiency

Quick revision checklist

Before attempting gas turbine cycles problems, confirm you can:
1. Open cycle: combustion replaces heat addition at constant P
2. Intercooling reduces compressor work; reheating increases turbine work
3. Back work ratio high (~40–50%) for gas turbines
Revise the solved examples in Engineering Thermodynamics — P.K. Nag and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Brayton cycle efficiency

Problem

A gas-turbine cycle has pressure ratio r_p = 10 and γ = 1.4. Find the air-standard efficiency.

Solution

η = 1 − 1/r_p^((γ−1)/γ) = 1 − 1/10^(0.2857) = 1 − 1/1.931 = 1 − 0.518 = 0.482, i.e. 48.2 %.

Conceptual check — Gas Turbine Cycles

Problem

In a Applied Thermodynamics semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of gas turbine cycles." What should a complete answer include?

Practice questions

Most-asked interview and GATE questions for this topic — expand any item for a model answer.

  1. 1
    What is Gas Turbine Cycles, and why does it appear in B.Tech / GATE syllabi?

    Model answer

    The Brayton cycle efficiency is η = 1 − 1/r_p^((γ−1)/γ), depending on the pressure ratio r_p. Net work is turbine minus compressor work; the high back-work ratio distinguishes gas turbines, per P.K. Nag.
  2. 2
    State the relation η_Brayton = 1 − 1/r_p^ and name each symbol.

    Model answer

    The governing relation is \eta_{Brayton} = 1 - \frac{1}{r_{p}}^. Write every symbol with SI units before substituting numbers.
  3. 3
    State the relation W_net = W_turb − W_comp and name each symbol.

    Model answer

    The governing relation is Wnet=Wturb−WcompW_{net} = W_{turb} - W_{comp}. Write every symbol with SI units before substituting numbers.
  4. 4
    State the relation r_p,opt = and name each symbol.

    Model answer

    The governing relation is rp,opt=r_{p},opt =. Write every symbol with SI units before substituting numbers.
  5. 5
    State the relation η_regen = 1 − and name each symbol.

    Model answer

    The governing relation is ηregen=1−\eta_{regen} = 1 -. Write every symbol with SI units before substituting numbers.
  6. 6
    Explain: Open cycle: combustion replaces heat addition at constant P

    Model answer

    Open cycle: combustion replaces heat addition at constant P — state the assumption range and one exam trap linked to this point.
  7. 7
    Explain: Intercooling reduces compressor work; reheating increases turbine work

    Model answer

    Intercooling reduces compressor work; reheating increases turbine work — state the assumption range and one exam trap linked to this point.
  8. 8
    Explain: Back work ratio high (~40–50%) for gas turbines

    Model answer

    Back work ratio high (~40–50%) for gas turbines — state the assumption range and one exam trap linked to this point.
  9. 9
    How would you correct this error in a viva: Ignoring compressor work and equating net work to turbine work (back-work ratio is large)?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  10. 10
    How would you correct this error in a viva: Using compression-ratio (volume) instead of pressure-ratio in the Brayton formula?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  11. 11
    How would you correct this error in a viva: Applying regeneration when T₄ < T₂ (heat would flow the wrong way)?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  12. 12
    How would you correct this error in a viva: Confusing the optimum pressure ratio for maximum work with that for maximum efficiency?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.

Exams & GATE

  • 1
    Plot Brayton on T-s — regeneration when T₄ > T₂.
  • 2
    Avoid: Ignoring compressor work and equating net work to turbine work (back-work ratio is large)
  • 3
    Avoid: Using compression-ratio (volume) instead of pressure-ratio in the Brayton formula
  • 4
    Avoid: Applying regeneration when T₄ < T₂ (heat would flow the wrong way)

📖 Standard books (India)

  • Engineering Thermodynamics — P.K. Nag

    Read: Syllabus unit

    The standard thermodynamics text in most Indian universities

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