02 / EXTERNAL ENERGY BALANCE
Where fuel energy goes
—Changes relative to incoming air, in the engine-fixed frame. Shaft work returned to the compressor is internal; it is not counted again here.
PROPULSION WORKBENCH
Gas Turbine Cycle & Thrust
Follow the energy. See what becomes thrust.
SINGLE-SPOOL TURBOJETSteady design points · generic teaching model
LIVE B · SCHEMATIC GAS PATHOne shaft · no bypass stream
Total temperature · K
Select a station. Colours use computed total conditions; geometry and marker speed are illustrative.
Net thrust—Momentum + pressure thrust
Specific thrust—Per kg/s of inlet air
Fuel consumption · TSFC—Fuel per unit net thrust
Fuel flow—Computed from heat addition
STATION 3
Compressor exit
03 / INSIDE THE ENGINE
The shaft closes the loop
The turbine supplies compressor power plus mechanical loss. There is no useful external shaft output in this turbojet.
04 / MOMENTUM BALANCE
What becomes net thrust
kN05 / ONE SOLUTION, CONNECTED VIEWS
Read the cycle
B · liveA · saved, dashed
Total temperature
Total temperature stays constant through an adiabatic nozzle. The exit static temperature is lower.
Total pressure
Compression raises total pressure. The turbine extracts work; irreversible losses reduce total pressure too.
Temperature–entropy view
Total-state stations joined by guides. The final hollow point is the static exit. This open-flow diagram is not a closed-cycle work-area plot.
Click a temperature or pressure curve to select a station. Both cases always share each chart’s axes.
06 / KEEP ONE DESIGN, CHANGE ANOTHER
A / B comparison
Save a reference A, then adjust B. The saved case will remain fixed for this session.
| Quantity | A · saved | B · live | B − A |
|---|
Compare all design settings
| Input | A · saved | B · live |
|---|
Model, equations & interpretation
A design-point workbench
A steady, generic single-spool turbojet with no bypass, bleed, cooling or accessory load. The inlet air mass flow is prescribed, and the required nozzle area is calculated. Changing the settings compares different designs; it does not reproduce a fixed engine’s throttle response or operating map.
Air and combustion products use the same constant representative properties: γ = 1.4, R = 287.05 J kg⁻¹ K⁻¹, cₚ = 1,004.675 J kg⁻¹ K⁻¹. Fuel heating value is 42.8 MJ/kg. Fuel sensible enthalpy is neglected. These simplifications affect absolute engine performance, especially at high temperature.
Altitude uses a dry, two-layer standard-atmosphere approximation in geopotential metres. Loss settings are illustrative teaching assumptions, not manufacturer data. Impossible combinations are rejected rather than drawn as valid solutions.
Three balances to keep separate
Burner: ṁₐ cₚ Tₜ₃ + ηᵦ ṁf Q = (ṁₐ + ṁf) cₚ Tₜ₄
Shaft: ηₘ ṁg cₚ (Tₜ₄ − Tₜ₅) = ṁₐ cₚ (Tₜ₃ − Tₜ₂)
Thrust: F = ṁg V₉ − ṁₐ V₀ + (p₉ − pₐ) A₉
Fuel mass is retained downstream of the combustor. The energy chart accounts for net exhaust thermal energy, net jet kinetic energy, fuel energy not transferred to the gas and mechanical loss. Compressor/turbine inefficiency generates entropy; it is not an extra external energy sink.
What the nozzle can establish
The convergent design reaches M = 1 when choked and can retain a positive pressure-thrust term. The perfectly expanded design sizes its exit so p₉ = pₐ; a convergent–divergent passage is required if its exit Mach exceeds one. Nozzle losses are represented by an upstream total-pressure recovery followed by isentropic expansion. No external shock cells, separation or internal two-dimensional flow field are solved.
Station convention on this page: 0 free stream; 2 compressor inlet; 3 compressor exit; 4 turbine inlet; 5 turbine exit; 8 nozzle supply after prescribed duct loss; 9 nozzle exit. Internal static quantities and shaft speed are not resolved.
Evidence and sources
Teaching basis: Engine performance and cycle analysis, pages 13–28. The notes’ small-fuel-mass and matched-nozzle idealisation is distinguished from this model’s retained fuel mass and convergent-nozzle option. All diagrams here are original.
Verification covers mass, shaft power, energy, nozzle limits, scaling, invalid designs and independent analytical landmarks. These are implementation checks; experimental validation remains open.
NASA · shaft matchingNASA · fuel balanceNASA · thrust equation