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Aerospace
Bypass ratio and fuel contribution to exhaust mass flow
Total mass flow leaving a bypass engine, whether the streams mix or leave separately: the core air flow mc, the bypass flow B·mc (bypass ratio B is relative to the core flow) and the fuel flow f·mc.
- Ref
- AER-52
- Rev
- v1
- Field
- Aerospace
- Result
- ṁex [kg/s]
The exhaust mass flow of a bypass engine is the sum of three streams: the core air ṁc, the bypass air B ṁc (the bypass ratio B is defined relative to the core flow) and the fuel f ṁc added in the combustor. It is the same whether the streams mix or leave separately. Bleed, leakage and other mass additions are not included.
Total mass flow leaving a bypass engine, whether the streams mix or leave separately: the core air flow mc, the bypass flow B·mc (bypass ratio B is relative to the core flow) and the fuel flow f·mc. No bleed, leakage or other mass addition.
Calculator
- Bypass air flow, B ṁc100 kg/s
- Fuel flow, f ṁc0.4 kg/s
- Total air flow, ṁc(1 + B)120 kg/s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The engine exhausts 120.4 kg/s, of which 83.06 % is bypass air, 16.61 % is core air and 0.3322 % is fuel.
- The fuel adds 2 % to the core flow, so exhaust flow exceeds inlet flow by that fraction of the core.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kg/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ṁc Core air mass flow | 1 to 200 kg/s | 6.02 | 1,204 | 1,198 | +10% | +10 % |
| B Bypass ratio | 0 to 15 | 20.4 | 320.4 | 300 | +10% | +8.31 % |
| f Fuel-to-core-air ratio | 0 to 0.05 | 120 | 121 | 1 | +10% | +0.0332 % |
Sweep of Bypass ratio
| Bypass ratio | Exhaust mass flow (kg/s) |
|---|---|
| 0 | 20.4 |
| 1.875 | 57.9 |
| 3.75 | 95.4 |
| 5.625 | 132.9 |
| 7.5 | 170.4 |
| 9.375 | 207.9 |
| 11.25 | 245.4 |
| 13.13 | 282.9 |
| 15 | 320.4 |
Sweep one variable
Variables and how each one contributes
Exhaust mass flow
What the equation gives you. Everything else feeds it.
Core air mass flow
The core air mass flow, in kg/s. Scales the exhaust flow in direct proportion. Raising it by 10 % (to 22) moves the result by +10 %, from 120.4 to 132.4 kg/s.
Bypass ratio
The bypass ratio, bypass flow over core flow. Raises the exhaust flow in direct proportion, by B ṁc. Raising it by 10 % (to 5.5) moves the result by +8.31 %, from 120.4 to 130.4 kg/s.
Fuel-to-core-air ratio
The fuel-to-core-air mass ratio. Adds the fuel mass, a small contribution. Raising it by 10 % (to 0.022) moves the result by +0.0332 %, from 120.4 to 120.4 kg/s.
Worked example with the values above
- Bypass flow: B ṁc = 5 × 20 = 100 kg/s.
- Fuel flow: f ṁc = 0.02 × 20 = 0.4 kg/s.
- ṁex = 20 + 100 + 0.4 = 120.4 kg/s.
Assumptions and limits
- Constant specific heats in each stream, adiabatic components and total-to-total efficiencies.
- Steady operation at one operating point, with no bleed and no leakage unless the page says so.
Common mistakes
- Mixing total and static states.
- Using a total-to-static efficiency where a total-to-total one is needed.
- Forgetting the fuel added to the turbine mass flow.
Statistics and uncertainty
Constant-cp cycle calculations are rough: cp rises from 1005 J/(kg·K) in cold air to about 1150 J/(kg·K) in hot gas, which shifts results by 5 % to 10 %. Component efficiencies from maps are good to 1 % to 2 % at design and worse off design.
Where it is used
- Matching compressors, combustors and turbines and finding fuel flow and power.
- Sizing engines and checking cycle designs.
Maths you need
- Isentropic efficiency: ideal work divided by actual work (or the reverse for a turbine)
- Total temperature: the temperature the gas would reach at rest
- Brayton cycle: compression, heat addition, expansion