USE CASE

A jet engine, from cycle to surge.

The Brayton cycle that powers every jet and gas-turbine plant, modelled as a single-spool turbojet: air is compressed, fuel burned, the gas expanded through a turbine that drives the compressor, and the rest dumped through a nozzle for thrust. The notebooks build it station by station, draw the compressor map, find the design point, spin the spool up, and walk into — then out of — the failure mode that defines engine control: compressor surge.

A compressor map — pressure ratio against corrected mass flow with speed lines, a surge line bounding a shaded surge zone, and the running line passing through the operating points safely below it

19.2 kN

design thrust (SL static)

23.8

TSFC mg/N·s

47.3%

thermal efficiency

1600 K

turbine-inlet temperature

25.8%

design surge margin

design notebooks

THE CYCLE

Five stations, one spool.

Air enters the inlet, the compressor raises its pressure twelvefold, the combustor burns fuel to 1600 K, the turbine expands the gas to drive the compressor, and the nozzle accelerates what's left to nearly a kilometre per second of exhaust. The one modelling point that makes a turbojet model right or useless: the turbine takes only enough enthalpy to drive the compressor — the work balance — which leaves a large pressure drop for the nozzle and hence real thrust. Prescribe the turbine expansion directly and the nozzle has nothing to work with and the engine makes no thrust; derive it from the compressor work and the design point lands at 19.2 kN and a textbook 23.8 mg/N·s fuel consumption.

A temperature-entropy diagram of the Brayton cycle, ideal versus real, with the lost-work area between them — The Brayton cycle on a T-s diagram: compression, constant-pressure heat addition to turbine-inlet temperature, expansion, and exhaust. The gap between the ideal and real cycles is the lost work — compressor and turbine inefficiency — that separates 47% thermal efficiency from the reversible ideal.

A compressor map with speed lines, a surge line bounding a shaded surge zone, the running line, and the operating points — The compressor map — the engine's defining chart. Each curve is a constant-speed line; the surge line bounds the shaded zone where flow breaks down; the running line threads the operating points the engine actually sits on, with a 25.8% margin to surge. Everything the engine does is a path on this map.

THE FAILURE MODE

Why engines have an acceleration schedule.

Slam the throttle and the engine can surge — a violent flow breakdown that can flame out or damage the machine. The reason is inertia: a fast fuel increase spikes turbine-inlet temperature while the spool is still at low speed, driving the operating point up the speed line and across the surge line. The model reproduces it exactly — an unrestrained fuel slam collapses surge margin to −59.6%, deep in surge — and shows the fix every real engine controller uses: a fuel-rate acceleration schedule that keeps the operating point on the running line and holds the margin at +23%.

The acceleration locus on the compressor map: a fast slam jumps up and crosses the surge line, while the scheduled accel stays on the running line clear of surge — Acceleration on the compressor map: the unrestrained fuel slam (purple) jumps up at low speed and crosses the surge line; the fuel-scheduled acceleration (green) stays on the running line, clear of surge, all the way to full power. The difference between those two paths is the engine's accel schedule.

A cycle design carpet plot of specific thrust against thrust-specific fuel consumption, locating the design point — The cycle design carpet: specific thrust against fuel consumption as pressure ratio and turbine temperature vary. Higher temperature buys specific thrust; higher pressure ratio buys efficiency; the design point is the chosen compromise on this trade surface.

Thrust lapse with altitude at Mach 0.8 — thrust falling to about a third of its sea-level value at 11 km — Off-design reality: thrust lapses to 35% of its sea-level value by 11 km as the air thins, while flight Mach number recovers some pressure through ram. The same cycle model that sized the engine tells you what it actually delivers at altitude and speed.

VALIDATION

Every spec is a number you can re-run.

The sign-off notebook re-derives each requirement from the same gas-path model the program builds up.

	Result	Requirement
Design thrust (SL static)	19.2 kN	R-01
Fuel consumption (TSFC)	23.8 mg/N·s	R-02
Turbine-inlet temperature	1600 K	≤ limit
Surge margin (scheduled accel)	+23.0%	≥ 0, slam −59.6%
Requirements verified	5 / 5	PASS

HONEST SCOPE

0-D, design-grade thermodynamics.

The engine is a 0-D / quasi-steady single spool, characterized by a self-consistent running line plus a surge line rather than a measured component map with beta-lines; the working fluid is ideal gas with cold and hot specific heats; the spool is lumped; the design point is sea-level static. That is exactly the fidelity preliminary cycle design and engine-control logic need first — sizing the cycle, choosing pressure ratio and turbine temperature, setting the acceleration schedule, and checking altitude lapse — on your own engine numbers, before a full component-matching or 3D aero model. Notebook-based; the cycle is causal, so there's no acausal network to compose.

Model your own engine cycle.

Book a walkthrough and we'll set up your design point, compressor and turbine characteristics, and run the cycle, surge and off-design studies live.

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