KEVOS® MAKEOS · Engineering
Gas Turbine (Brayton) Cycle Check with Regenerator (Net Power, Back-Work Ratio, Efficiency)
What net power, back-work ratio and thermal efficiency does this gas-turbine cycle give with real compressor and turbine efficiencies, how much does a regenerator add, and does the net power meet the demand?
Cold-air-standard gas-turbine (Brayton) cycle with real compressor and turbine efficiencies and an optional regenerator: the temperatures around the cycle, the compressor, turbine and net work, the back-work ratio, the thermal efficiency with and without the regenerator, the heat input and the net power for the air flow, against the power you need.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Compressor inlet temperature | °C | Air temperature at the compressor inlet: ambient air temperature at the intake. |
| Compressor pressure ratio (P₂ ÷ P₁) | :1 | Compressor pressure ratio from the machine data sheet (outlet ÷ inlet absolute pressure). |
| Turbine inlet temperature | °C | Turbine inlet (firing) temperature from the maker’s data or the control system. |
| Compressor isentropic efficiency | % | Compressor isentropic efficiency from the maker’s performance data or a test. |
| Turbine isentropic efficiency | % | Turbine isentropic efficiency from the maker’s performance data or a test. |
| Regenerator effectiveness (0 = no regenerator) | % | Regenerator (recuperator) effectiveness from its data sheet: the share of the largest possible temperature rise of the compressed air that it achieves. Enter 0 for no regenerator. |
| Gas and flow | ||
| Specific heat of the gas at constant pressure | kJ/kg·K | Specific heat of the gas at constant pressure: 1.005 kJ/kg·K for air at room temperature. |
| Specific heat ratio of the gas (cp ÷ cv) | Ratio of specific heats: 1.4 for air at room temperature. | |
| Air mass flow | kg/s | Air mass flow through the machine from the maker’s data or measurement. |
| Demand | ||
| Net power required | kW | Net shaft power you need from the cycle. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Compressor inlet temperature
- What it is
- The temperature of the air entering the compressor, normally the ambient air temperature at the intake.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 200 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter inlet raises the compressor work and lowers the net work and efficiency.
- Get it right
- Gas turbines lose output on hot days; check at the hottest site condition that matters.
What this means: Compressor pressure ratio (P₂ ÷ P₁)
- What it is
- The absolute pressure leaving the compressor divided by the absolute pressure entering it, which sets the temperature rise in compression and fall in expansion.
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 1.1 :1 to 60 :1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes both compressor and turbine work; the regenerator benefit falls as the ratio rises.
- Get it right
- Use absolute pressures; a gauge reading divided by another gauge reading gives the wrong ratio.
What this means: Turbine inlet temperature
- What it is
- The temperature of the hot gas entering the turbine after the combustor, the highest temperature in the cycle.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 100 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1100 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter turbine inlet raises the turbine work, net power and efficiency.
- Get it right
- Use the turbine inlet (firing) temperature, not the exhaust temperature shown on many panels.
What this means: Compressor isentropic efficiency
- What it is
- The ideal (isentropic) compressor work divided by the actual work for the same pressure ratio, which measures how much extra work friction and leakage cost.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 30% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower efficiency raises the compressor outlet temperature and work, cutting net power.
- Get it right
- Fouled compressors lose several points; washed or new machines are near the maker’s figure.
What this means: Turbine isentropic efficiency
- What it is
- The actual turbine work divided by the ideal (isentropic) work for the same pressure ratio, which measures the losses in the expansion.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 30% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 88% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower efficiency raises the exhaust temperature and cuts turbine and net work.
- Get it right
- Use the maker’s figure at the operating point; it falls at part load.
What this means: Regenerator effectiveness (0 = no regenerator)
- What it is
- How much of the largest possible heating of the compressed air by the turbine exhaust the regenerator actually achieves; zero means the machine has no regenerator.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher effectiveness lowers the fuel heat needed and raises the efficiency; net work does not change.
- Get it right
- It is only used when the exhaust is hotter than the compressed air; the tool reports when it is not.
Gas and flow
What this means: Specific heat of the gas at constant pressure
- What it is
- The energy needed to raise one kilogram of the gas by one kelvin at constant pressure, which turns temperature changes into work and heat.
- Units and format
- Enter a number in kJ/kg·K: kilojoules per kilogram per kelvin. The form accepts 0.5 kJ/kg·K to 20 kJ/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.005 kJ/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All work, heat and power values scale in proportion; temperatures and efficiency do not change.
- Get it right
- Air is about 1.005 kJ/kg·K at room temperature and rises when hot; keep it consistent with k.
What this means: Specific heat ratio of the gas (cp ÷ cv)
- What it is
- The ratio of the specific heats of the gas, which sets how much the temperature changes for a given pressure ratio in compression and expansion.
- Units and format
- Enter a plain number with no unit. The form accepts 1.05 to 1.67. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher ratio increases the temperature change per unit pressure ratio in both machines.
- Get it right
- Use 1.4 for cold air; hot combustion gas is nearer 1.33.
What this means: Air mass flow
- What it is
- The mass of air passing through the compressor each second, which multiplies the work per kilogram into power.
- Units and format
- Enter a number in kg/s: kg/s. The form accepts 0.001 kg/s to 1000 kg/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 kg/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Net power and heat input rise in proportion; efficiency does not change.
- Get it right
- Mass flow falls on hot days and at altitude even if the volume flow stays the same.
Demand
What this means: Net power required
- What it is
- The net shaft power the gas turbine must deliver to the generator, compressor or other load it drives.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line of the power check.
- Get it right
- Include gearbox and generator losses if the demand is an electrical output.
Method and formulas
- Compressor: T₂ₛ = T₁ r_p^((k−1)/k) and T₂ = T₁ + (T₂ₛ − T₁) ÷ η_c; turbine: T₄ₛ = T₃ ÷ r_p^((k−1)/k) and T₄ = T₃ − η_t (T₃ − T₄ₛ), temperatures in kelvin.
- Work: w_c = cp (T₂ − T₁), w_t = cp (T₃ − T₄), w_net = w_t − w_c; back-work ratio = w_c ÷ w_t.
- Regenerator (only when T₄ > T₂): air to the combustor T₅ = T₂ + ε (T₄ − T₂); heat input q_in = cp (T₃ − T₅); exhaust after the regenerator T₆ = T₄ − (T₅ − T₂).
- Efficiency η = w_net ÷ q_in; net power = ṁ w_net; heat input = ṁ q_in.
- Example: 5 kg/s of air at 15 °C, a pressure ratio of 10, 1,100 °C at the turbine, 85 % and 88 % component efficiencies and a 75 % regenerator give 1,341.6 kW net at 42.43 % efficiency (34.7 % without the regenerator), meeting a 1,200 kW demand.
Limitations
- Cold-air standard: constant specific heats, no fuel mass added, no pressure loss in the combustor, regenerator, intake or exhaust, and no cooling or leakage air.
- Real gas turbines also lose output at high ambient temperatures and altitudes through lower air density, which only the mass flow you enter allows for.
- A screening model of the cycle, not a turbine selection or performance guarantee; the maker’s performance data and qualified review govern real plant.
- Example values are illustrations. Replace them with values for your actual machine.
Typical uses
- Screen the net power and efficiency of a small gas turbine or microturbine at a pressure ratio and firing temperature
- See whether a recuperator or regenerator is worth fitting at a given pressure ratio
- Show how compressor and turbine efficiencies eat into net work when the back-work ratio is high
Who it is for
- Mechanical and energy engineers
- Cogeneration and power-plant engineers
- Engineering students and trainers
What you get
- Compressor outlet, turbine exhaust, air-to-combustor and final exhaust temperatures
- Compressor, turbine and net work per kilogram and the back-work ratio
- Thermal efficiency with and without the regenerator
- Heat input and net power against the demand
Interpreting the result
- A back-work ratio near or above 50 % means small losses in the compressor or turbine take a large share of the net work.
- A regenerator helps most at low pressure ratios, where the turbine exhaust is much hotter than the compressed air; at high pressure ratios the tool reports that it would cool the air instead.
Before relying on the result
- Compare with the maker’s rated output and heat rate at site conditions.
- Check that the recuperator’s pressure losses, which this model ignores, do not wipe out the gain.
References
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach, 5th edition (McGraw-Hill, 2006), chapter 9 (sections 9-8 and 9-9: Brayton cycle, deviation from the ideal cycle, regeneration) and section 7-12 (isentropic efficiencies). Method reference; no tables, figures or examples are reproduced.
- Saravanamuttoo H. I. H., Rogers G. F. C. and Cohen H., Gas Turbine Theory (Pearson): simple and recuperated cycle performance with component efficiencies.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Gas turbines and the Brayton cycle
In On-Site Power and Heat by the Numbers
What it covers: How a gas turbine turns fuel into shaft power: the Brayton cycle, pressure ratio, turbine inlet temperature, the back-work ratio, component efficiencies and why hot days cut output.
Worked example · Library collection
Engines after steam: internal combustion, diesel, gas turbines and matching technology to the duty
In How Engineering Shaped Industry: Power, Networks and the Modern Era
What it covers: Petrol, diesel and gas turbine engines each won where their strengths matched the work. How they developed, why efficiency depends on compression and temperature, and how to choose power.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.