Inducer Erosion and NPSH Margin in a LOX Turbopump
A 62 kg/s liquid-oxygen turbopump for a 10-tonne-thrust engine runs at 15,000 rpm behind a three-blade helical inducer. LOX enters the inducer eye at 92 K with a static pressure of 0.34 MPa absolute; the vapour pressure at that temperature is 0.13 MPa and the density is 1130 kg/m3. The inlet duct is 100 mm internal diameter. After the third hot-fire test (220 s cumulative) the borescope shows pitting on the suction surface of all three inducer blades in the outer 15% of span, discharge head has fallen 3.5%, and the inlet pressure transducer now shows a line at 250 Hz together with broadband energy between 1 and 4 kHz that was absent on the first two tests. Pump speed and discharge flow are unchanged. The team proposes to cure the problem by raising the tank pressure so that inducer-inlet static pressure becomes 0.40 MPa. Propellant tank mass is tightly budgeted and every 0.01 MPa of pressurisation costs hardware.
1. Compute the NPSH available at the pump inlet and the suction specific speed, and rule on whether the cavitation diagnosis is supported by the hardware evidence.
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NPSH available
Static component: (0.34 - 0.13) x 10^6 / (1130 x 9.81) = 210,000 / 11,085 = 18.9 m.
Velocity head at the inlet: v = 62 / (1130 x pi x 0.05^2) = 62 / 8.88 = 6.99 m/s; v^2/2g = 2.5 m.
NPSH_a at the flange ≈ 18.9 + 2.5 = 21.4 m.
Suction specific speed (SI form, S = omega x sqrt(Q) / (g x NPSH)^0.75)
- Q = 62/1130 = 0.0549 m3/s, sqrt(Q) = 0.234
- omega = 2 x pi x 250 = 1570.8 rad/s, numerator = 368.1
- (9.81 x 21.4)^0.75 = (209.9)^0.75 = 55.2
- S = 368.1 / 55.2 = 6.67
Diagnosis: supported. Three independent pieces of evidence agree. First, S of about 6.7 is above the 4.5–5.5 band in which a conventional inducer keeps a healthy breakdown margin, so the pump is operating in the regime where the leading-edge suction peak drops to vapour pressure. Second, the damage is where theory puts it: the suction surface, outer 15% of span, where relative velocity and the minimum pressure coefficient coincide. Third, the 250 Hz line is exactly one-per-revolution and the 1–4 kHz broadband energy on the inlet transducer is the signature of collapsing bubbles, not of a mechanical rub (which would grow as a shaft-rate harmonic family rather than broadband). A 3.5% head loss with unchanged flow is consistent with blade blockage and altered incidence from the eroded leading edges.
2. Quantify what the proposed 0.06 MPa pressurisation buys and evaluate it as a fix.
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Gain in NPSH: 0.06 x 10^6 / (1130 x 9.81) = 5.4 m, taking NPSH_a from 21.4 to 26.8 m.
Effect on suction specific speed: S = 368.1 / (9.81 x 26.8)^0.75 = 368.1 / (262.9)^0.75 = 368.1 / 65.3 = 5.64.
Assessment: the fix moves S from 6.67 to 5.64 - still at the top of, or above, the range where this inducer geometry was designed to run. It buys 5.4 m of margin for a permanent pressurisation mass and structural penalty on the tank, and it leaves no margin for the two things that always get worse in flight: inlet line losses at high flow, and the scatter of vapor pressure with temperature. It is a palliative, not a cure.
A better sequencing is to find out what actual breakdown NPSH this inducer has, then buy margin against that number rather than against a rule of thumb. The cheap lever worth computing first is inlet diameter: opening the duct from 100 mm to 120 mm drops the velocity from 6.99 to 4.85 m/s and recovers 2.5 - 1.2 = 1.3 m of NPSH by velocity head alone, with no tank mass penalty, at the cost of a longer, heavier line. Also check whether the running speed can be ramped through the low-NPSH band during start, because NPSH requirement scales with N^2 while tank pressure does not.
3. Recommend the test that decides the issue and the design changes that follow from it. Be explicit about the acceptance criterion you would impose before the next hot-fire.
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Deciding test: a cold-flow cavitation test on the inducer alone (water at the same flow coefficient and tip speed, or LN2 for a closer density and thermal-suppression match), in which inlet pressure is progressively reduced at constant speed and flow until head falls by 3% or the 250 Hz / broadband signature appears. That gives the breakdown NPSH as a measured number, not a correlation. Then set the operating requirement as breakdown NPSH times a margin - 1.3 to 1.5 is the usual band for a rocket turbopump inducer where the inlet is fed by a pressurised tank - and check that the flight inlet pressure minus worst-case line losses, minus the velocity-head term, still clears it at every flow and temperature in the envelope.
Acceptance before the next hot-fire: 220 s of operation with no increase in the 1–4 kHz inlet broadband energy above the first-test baseline, no new 250 Hz line, and head within 1% of the pre-erosion value. Erosion is cumulative; a test that merely produces 'less damage' is not a pass.
Design changes worth the schedule: increase the inducer inlet area (lower axial velocity and lower relative inlet velocity), reduce tip clearance at the leading edge, re-profile the leading-edge sweep to unload the tip, and if the flow coefficient allows it, add a splitter blade to shorten the effective blade passage. Speed reduction at the same flow is usually the single largest NPSH win, since the requirement falls with N^2, and it is worth checking whether the turbine can pass the same power at lower speed. Choose tank pressurisation only after the measured breakdown NPSH shows how much is genuinely needed.