Compressor Surge on a Hot-Day Slam Acceleration
The 9-stage high-pressure compressor of a medium-bypass turbofan surges twice during a slam acceleration from ground idle on a day 25 °C above ISA; on a standard day the same schedule is clean. Telemetry at the instant of surge shows 84% N2, corrected compressor flow 21.6 kg/s, compressor pressure ratio 6.80 and fuel flow 2.60 kg/s. Rig data give a surge-line pressure ratio of 7.20 at that corrected flow, and the company requires a 12% surge margin, defined as SM = PR_surge/PR_op − 1 at matched corrected flow. Local sensitivity at this operating point is dPR/df ≈ 2.5 per (kg/s). The variable stator vanes are scheduled on physical N2 with a 0.4 s lag, and the handling bleed closes at 82% N2. The acceleration fuel schedule is a fixed ramp that does not reference compressor pressure ratio. Full-power acceleration takes 4.5 s on a standard day.
1. Compute the surge margin at the recorded operating point and determine the fuel flow that would satisfy the 12% requirement.
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At matched corrected flow the definition reduces to a pressure-ratio ratio:
SM = PR_surge/PR_op − 1 = 7.20/6.80 − 1 = 0.0588, i.e. 5.9%
That is roughly half the required 12%, so the surge is a margin shortfall, not an anomaly to be explained by sensor error or a one-off.
The maximum permissible pressure ratio at this corrected flow is
PR_max = PR_surge/1.12 = 7.20/1.12 = 6.43
The operating point must therefore come down by ΔPR = 6.80 − 6.43 = 0.37. With dPR/df = 2.5 per (kg/s):
Δf = −0.37/2.5 = −0.148 kg/s
so the schedule may command at most 2.60 − 0.15 = 2.45 kg/s at this condition, a cut of about 5.7% of acceleration fuel.
Two caveats. First, the margin must be checked along the whole transient, not only at 84% N2, because the operating line is closest to the surge line where the VSVs are most out of position; 84% is simply where this event happened to be captured. Second, the 12% requirement already contains the scatter allowance for engine-to-engine variation, so the schedule change must be validated on the worst-build engine, not the test engine.
2. Explain why the surge occurs on a hot day but not on a standard day, using corrected parameters, and state what must change in the control schedule.
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Compressor behaviour collapses onto corrected maps in N2/√θ and ṁ√θ/δ. On a +25 °C day, T1 ≈ 313 K, so θ = 313/288.15 = 1.086 and √θ = 1.042. At the same physical 84% N2 the machine is running at a corrected speed of 84/1.042 = 80.6% - effectively a different speed line, roughly 3.4 points lower.
Because the VSV schedule is a function of physical N2 (with a 0.4 s lag), the vanes at 84% physical N2 are positioned for the standard-day 84% line, i.e. they are too far closed for the correct 80.6% corrected-speed line. Front stages run at high incidence, the front-stage flow capacity falls, and the rear stages choke - the classic mechanism that collapses surge margin at low corrected speed. The same lag argument applies to the handling bleed, which closes at 82% physical N2: on the hot day it closes while the machine is still effectively at 78.7% corrected speed, removing stability bleed when it is still needed.
The fuel schedule makes it worse because it is a fixed ramp. At high inlet temperature the engine accelerates on the same fuel ramp but with less air mass flow, so the fuel-to-air ratio and hence PR rise faster relative to the available surge margin.
Required changes: schedule the VSVs and the handling bleed on corrected speed N2/√θ rather than physical N2; close the bleed on a corrected speed or PR criterion, not a fixed N2; and make the acceleration fuel schedule PR-limited (a closed-loop accel schedule referencing compressor pressure ratio or surge margin), so the fuel authority is bounded by margin rather than by time.
3. Assuming the acceleration fuel cut you computed is adopted, estimate its cost in spool-up time, and weigh that against the alternative of extending handling bleed. State which you would release first and why.
Read the worked answer
The acceleration is driven by the excess of turbine work over compressor work, which is roughly proportional to the excess fuel above the steady-state schedule. Cutting the excess fuel by 5.7% at the governing condition increases the acceleration time by roughly the same proportion, ignoring the change in compressor efficiency: 4.5 s × 1.057 ≈ 4.75 s, about 0.25 s slower over the full idle-to-max transient. On a go-around or a wave-off this is at the edge of acceptability but survivable; in normal line operation it is invisible.
The handling-bleed alternative: keeping the bleed open to 88% N2 instead of 82% costs about 1–2% in core thrust and specific fuel consumption over that band, and raises turbine entry temperature slightly because the extra bleed is dumped overboard after being compressed. Over an engine life this is a real fuel burn penalty, and it acts on every hot-day acceleration, not only on the slam case.
Release order:
- Fuel schedule first - a software change to the acceleration schedule with a PR-based limit. It costs about 0.25 s of transient time, no hardware, no fuel-burn penalty in steady state, and it directly addresses the mechanism that removes margin (excess fuel raising PR).
- VSV and bleed scheduling on corrected speed second - also software but requires a validated corrected-speed signal and re-rigging checks across the envelope; it recovers the margin that the hot day actually removed.
- Hardware last - a larger handling bleed valve or a re-staggered VSV row is only justified if the flight envelope still shows margin shortfalls after the schedule fixes.
Before release, re-audit margin at the corners of the envelope: hot day at low corrected speed with the bleeds closed is the critical case, not the sea-level static slam that produced this event.