Regenerative Cooling Anomaly: High Pressure Drop with High Wall Temperature
A 10 kN LOX/RP-1 thrust chamber uses 60 milled cooling channels, each 1.5 mm wide and 4.0 mm deep, closed out by electroforming; the hot-gas wall is 1.0 mm of Cu-Cr-Zr. Chamber pressure is 7.0 MPa. RP-1 enters the jacket at 300 K and 3.2 kg/s. The design model gives a coolant pressure drop of 2.8 MPa, a coolant exit temperature of 523 K and a peak hot-wall temperature of 640 K, and that 640 K is the basis of the creep-life calculation. The first 30 s hot-fire gives a measured coolant pressure drop of 3.9 MPa, an exit coolant temperature of 540 K, and readings of 795 K and 812 K from the two wall thermocouples nearest the throat. Thrust and mixture ratio are within 1% of nominal, and the coolant flow meter reads within 2% of 3.2 kg/s. The pressure transducer is new; both thermocouples were replaced after an earlier failure and are installed in the same groove pattern as before. Borescope of the inlet manifold shows no obstruction, and no channel has yet been sectioned.
1. Use the coolant energy balance to determine the actual heat load, and quantify how much of the 160 K wall-temperature rise it can explain.
Read the worked answer
Heat load from the coolant (take cp of RP-1 as 2100 J/kg.K)
- Measured: q = 3.2 x 2100 x (540 - 300) = 1.61 MW
- Design: q = 3.2 x 2100 x (523 - 300) = 1.50 MW
- Excess: +7.6%
How much wall rise that explains
The wall temperature is set by Tw = Tcoolant + q''/h. Take the design driving temperature difference at the throat as 640 - 420 = 220 K (local bulk near the throat is above the inlet value). A 7.6% rise in heat flux with unchanged h raises that difference by 7.6%, to 237 K, giving Tw of about 657 K - roughly 17 K of the observed rise.
The measured rise is 795 to 812 K against 640 K, i.e. about 160 K. So the energy balance explains only about a tenth of it.
What the rest requires
If q'' is up 7.6% and Tw is up by 160 K, then h must have fallen by roughly 220/380 = 0.58, i.e. to 58% of the design value. Since h scales as Re^0.8, that corresponds to a local flow of about 0.58^(1/0.8) = 0.58^1.25 = 0.51, i.e. half the design flow in the region where those thermocouples sit.
That is the key number: the wall temperature is telling you that coolant is not reaching that region, not that the engine is making more heat. A total flow of 3.2 kg/s is confirmed by the flow meter and by the bulk temperature rise, so any flow deficit has to be local - a partially blocked or over-narrowed channel - or the h correlation is being applied outside its validity, or the thermocouples are not reading what they claim to read.
2. The pressure drop and the wall temperature point in opposite directions. What does that tell you, and what is the first thing you check?
Read the worked answer
The inconsistency, stated plainly
A 39% rise in pressure drop at constant total flow means the flow passages are effectively smaller or rougher than modelled. Either way the coolant velocity in those channels goes up, and h goes up with it (h proportional to Re^0.8), which would drive the wall temperature down. The measured wall temperature went up by 160 K, which requires h to fall to about 58% of design. There is no single geometric change that produces both a higher pressure drop and a lower heat-transfer coefficient at the same mass flow. Two measurements that cannot both be right about the same hardware is the classic signature of an instrumentation or data-reduction problem.
First thing to check: the pressure tap. A 39% offset is exactly what a partially plugged or gas-filled tap produces - coke or a trapped bubble in the sense line adds a large, spuriously high differential and is easy to miss because the transducer itself is new. Purge and re-zero the sense line, verify against a second tap, and check the calibration record of the transducer against a deadweight tester.
Second: the thermocouples. Both were replaced, and both are installed in grooves. A thermocouple whose bead sits off the hot wall, with poor contact or the wrong groove depth, reads low, not high; so the high readings are more likely to be real, or to be reading a genuine local hot streak from a partially blocked channel. Verify by comparing the two readings' time histories during the transient - real channel blockage produces a plateau or a divergence as the wall heats, while a bad junction tends to track oddly or drift.
Only after both instruments are cleared would I section a channel or CT-scan the jacket.
3. Using the RP-1 bulk thermal-stability limit of about 600 K, quantify the coolant exit-temperature margin and its sensitivity. What do you do before the next hot-fire?
Read the worked answer
Margin
Exit bulk temperature is 540 K against a 600 K coking limit: 60 K of margin, and only 77 K above the design value of 523 K. That is thin, and it degrades fast.
- Heat load up 10% (1.61 to 1.77 MW): exit temperature rises by 0.10 x 240 = 24 K, to 564 K.
- Flow down 10% (3.2 to 2.88 kg/s) at the same heat load: exit rise goes as 1/flow, so the 240 K rise becomes 240/0.9 = 267 K, giving exit 567 K.
- Both together (a plausible worst case in a long burn as the tank drains and the pump wears): 1.1/0.9 = 1.22 x 240 = 293 K rise, exit 593 K - essentially at the coking limit.
So a 30 s test looks safe and a 300 s mission burn does not. The margin must be evaluated at end-of-burn, not at the measured condition.
Before the next hot-fire
- Clear the instrumentation: purge, re-zero, calibrate the pressure transducer, and verify thermocouple installation depth and contact against the drawing; a re-run of the coolant energy balance with a trustworthy pressure drop is worth more than any redesign.
- Add a second, independent wall-temperature measurement near the throat - a resistance temperature detector or an infrared pyrometer through a window on a dedicated test article.
- Section or CT-scan one channel in a scrapped article of the same build to establish the actual channel width, depth and surface finish, and compare with the milled and electroformed drawing.
- Only if the anomaly survives all three: raise coolant flow, re-profile the throat channels, or change the wall material. Do not raise flow to compensate for a measurement; it costs pressure drop you do not have.