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Heat Engine Simulator

Brayton Cycle Simulator — Thermal Efficiency of a Gas Turbine

Visualize the Brayton cycle, the ideal cycle of gas turbines and jet engines. Change the pressure ratio, specific heat ratio, inlet temperature and turbine inlet temperature to learn how the T-s diagram and efficiency curve respond.

Parameters
Pressure ratio r_p = P_2/P_1
—
Specific heat ratio γ
—
Inlet temperature T_1
K
Turbine inlet temp T_3
K

Air-standard cycle with constant specific heat c_p = 1.005 kJ/(kg·K) is assumed.

Results
—
Thermal efficiency η
—
Compressor outlet T_2
—
Turbine outlet T_4
—
Net work w_net
T-s Diagram (Temperature-Entropy)

1 to 2 isentropic compression / 2 to 3 isobaric heating / 3 to 4 isentropic expansion / 4 to 1 isobaric rejection (light lines = isobars P_1, P_2)

Thermal Efficiency vs Pressure Ratio η(r_p)

X axis = pressure ratio r_p / Y axis = thermal efficiency η (yellow dot = current r_p, η = 1 − 1/r_p^((γ−1)/γ) at the current γ)

Theory & Key Formulas

The Brayton cycle is the ideal cycle of a gas turbine made of compressor, combustor and turbine, analyzed as the air-standard cycle with air as the working fluid.

Temperature ratio of the isentropic compression, written with the exponent (γ−1)/γ:

$$\frac{T_2}{T_1} = r_p^{(\gamma-1)/\gamma}, \qquad \frac{T_3}{T_4} = r_p^{(\gamma-1)/\gamma}$$

Thermal efficiency of the ideal cycle, set only by pressure ratio r_p and specific heat ratio γ:

$$\eta = 1 - \frac{1}{r_p^{(\gamma-1)/\gamma}}$$

Heat input (combustor) and net work (turbine work minus compressor work):

$$q_\text{in} = c_p (T_3 - T_2), \qquad w_\text{net} = c_p\bigl[(T_3 - T_4) - (T_2 - T_1)\bigr]$$

Efficiency rises monotonically with pressure ratio, but with a TIT cap there is an optimum pressure ratio that maximizes net work.

What is the Brayton Cycle Simulator

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What kind of cycle actually runs inside a jet engine or a power-plant gas turbine?
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That is the Brayton cycle. Roughly speaking, it cycles through "compress, burn, expand, exhaust". Air is squeezed by the compressor, fuel is added in the combustor to heat it, the turbine expands it to pull out work, and the rest is dumped as exhaust. In the T-s diagram in the simulator above you can see the four states forming a box.
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Raising the "pressure ratio" slider raises the efficiency. Is there a limit to how high we can push it?
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In theory the higher the pressure ratio the higher the efficiency. The formula $\eta = 1 - 1/r_p^{(\gamma-1)/\gamma}$ tends to 1 as r_p grows. But real machines do not let you go that easily. The compressor outlet temperature T_2 also rises, which shrinks the temperature gap (T_3 − T_2) available for combustion, so the net work actually drops. The "best efficiency" pressure ratio and the "best work" pressure ratio are different. Sweep r_p from 4 to 50 in the simulator and watch the w_net card.
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I have heard that the turbine inlet temperature (TIT) is also crucial. Why?
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In the ideal formula efficiency depends only on r_p and γ, but the net work w_net depends directly on the gap between TIT and T_1. The higher the TIT, the larger the enthalpy drop available in the turbine, so the same flow produces more output. Gas turbine history is essentially the history of blade alloys, internal cooling and thermal-barrier coatings able to withstand ever higher TIT. Modern aero engines exceed 1700 degrees C TIT.
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How is it different from the Rankine cycle (steam turbine)?
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The working fluid and whether there is a phase change. Brayton uses gas only, Rankine uses the water-steam phase change. Gas turbines start fast and are easier to make compact, but the exhaust is hot. That hot exhaust is "wasted heat". Using it to drive a steam turbine is the combined-cycle (CCGT) approach, with overall efficiency above 60 percent. Today's high-efficiency thermal plants are mostly built this way.

Frequently Asked Questions

In the air-standard cycle that assumes air as an ideal gas with constant specific heat, lossless isentropic compression and expansion, and isobaric combustion, the thermal efficiency is exactly η = 1 − 1/r_p^((γ−1)/γ) and depends only on the pressure ratio r_p and the specific heat ratio γ. Real machines lose 5 to 15 efficiency points to blade losses, combustor pressure drop and air leakage, so at the same r_p the effective efficiency is lower.
With turbine inlet temperature T_3 fixed, the pressure ratio that maximizes net work w_net = c_p[(T_3−T_4) − (T_2−T_1)]. Defining τ = T_3/T_1, the optimum is r_p,opt = τ^(γ/(2(γ−1))). For example with τ = 5 (T_1=290, T_3=1450) and γ=1.4 we get r_p,opt ≈ 11.2. The pressure ratio that maximizes efficiency is different and increases monotonically with r_p.
Aero engines prioritize thrust-to-weight, so they push for light weight and high pressure ratio (modern engines reach 50:1). Power gas turbines prioritize fuel economy and durability, accept a lower pressure ratio, and chase overall efficiency through the combined cycle. Famous aero examples are CFM56 and GE90; representative power turbines are GE 9HA and Mitsubishi M501J. Power turbines run for thousands of hours, so maintainability is a major design factor.
In the regenerative Brayton cycle, the turbine exhaust preheats the compressor outlet air. It only helps when T_4 > T_2, which holds at low pressure ratios. With regeneration the efficiency becomes η_regen = 1 − (T_1/T_3)·r_p^((γ−1)/γ), giving a large boost in the low-r_p region. This configuration is common in microturbines and high-efficiency cogeneration units.

Real-World Applications

Aero jet engines: Turbojets, turbofans and turboprops are all built on the Brayton cycle. The compressor-combustor-turbine core is the same; the difference is whether the output is taken as the kinetic energy of a jet or as shaft rotation. Modern turbofans achieve pressure ratios of 50:1, TIT above 1700 degrees C and propulsive efficiency above 70 percent.

Power-generation gas turbines: Burning natural gas, these are the heart of modern thermal plants. They start fast and follow load well, so they play a key role in grids with strong demand swings. In a combined-cycle gas turbine (CCGT) the exhaust heat drives a steam turbine and the overall efficiency exceeds 60 percent, the dominant form of new thermal generation today.

Mechanical drive and pipeline compressors: Long-distance natural-gas pipelines and offshore platforms use stand-alone gas turbines to drive the booster compressors and large pumps. Independent of the electrical grid, they support remote energy infrastructure with large continuous power.

Microturbines and small distributed generation: Small gas turbines in the 30 to 300 kW range, often combined with a regenerator, are used as cogeneration units in commercial buildings, hospitals and factories. Designed at low pressure ratios of 4 to 5 to maximize the regenerator benefit, total energy efficiency (electric plus heat) above 80 percent is achievable.

Common Misconceptions and Cautions

The most common misconception is to think that "raising the pressure ratio always raises the engine output". Thermal efficiency η does increase monotonically with r_p, but the net work w_net follows a hump-shaped curve and peaks at some optimum pressure ratio r_p,opt. Beyond that point the work consumed by the compressor grows so much that the gap to the turbine work shrinks. Sweep the pressure ratio from 4 to 50 in the simulator and watch the w_net card start to fall in the upper range. "Best efficiency" and "best work" are different optimization problems.

The next most common error is to forget that this simulator shows the ideal air-standard efficiency, not the real efficiency of a hardware machine. Real turbomachines have compressor efficiency of 85 to 90 percent, turbine efficiency of 88 to 92 percent, combustor pressure drop of 3 to 5 percent, plus leakage and mechanical losses, so the actual efficiency falls 5 to 15 points below the ideal value. An ideal η of 50 percent typically becomes about 40 percent on a real machine. Catalog efficiency figures for real gas turbines already include all of these losses.

Finally, watch out for the limit of treating γ (specific heat ratio) as constant. Air at room temperature has γ ≈ 1.40, but the hot combustion gas has γ ≈ 1.30. Sliding γ from 1.20 to 1.50 in the simulator visibly changes the efficiency card. Accurate performance prediction needs a "variable specific heat" analysis with separate cold-side and hot-side γ; the simulator output should be taken as a first-cut estimate. Ideal cycle, then loss corrections, then field calibration: this layered approach is the standard engineering workflow.

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