Whose measurements these are
R. K. McCardell, D. I. Herborn and J. E. Houghtaling set down what the reactor did, and how sure they were of each number.
They wrote for the Atomic Energy Division of Phillips Petroleum Company, under contract to the U.S. Atomic Energy Commission, and their report of March 1969 covers eighty surges of power. Three of its tables give seventy of them, cold and hot, with a standard deviation beside the values, and that care is what lets a model be compared with their work more than half a century later.
- The authors
- R. K. McCardell, D. I. Herborn and J. E. Houghtaling
- Written for
- Phillips Petroleum Company, Atomic Energy Division, under contract to the U.S. Atomic Energy Commission, Idaho Operations Office
- The report
- Reactivity Accident Test Results and Analyses for the SPERT III E-Core: A Small, Oxide-Fueled, Pressurized-Water Reactor. Report IDO-17281, March 1969.
- Where it is published
- The U.S. Department of Energy’s Office of Scientific and Technical Information: doi.org/10.2172/4792676
- The report’s own thanks
- The authors thank M. Ishikawa, G. A. Mortensen, R. K. Stitt and M. W. King, and J. P. Campbell, J. F. Scott and W. A. Eisenbarth of the Oxide Core Kinetics Group, and write that the programme took the efforts of many people.
What happened
Eighty times, on purpose, a reactor was given a sudden surge of power. Every time it came through unharmed.
Some tests began cold, with the reactor barely running. Others began hot, at 1500 psig with the water flowing: from a startup, from hot standby at about 1 megawatt, or from operating power at 19. Each time a rod was ejected, and the power climbed.
How do you learn what a power reactor does in an accident without having the accident? In the 1960s one answer was to build a small reactor that could take it, and to give it the surge on purpose.
The E-core of SPERT III held 1392 rods of uranium oxide. Its tests ran in five series: thirty from a cold start, fifteen hot at 260 °F, seventeen hot at 500 °F, five from hot standby and three from operating power. In each, the fuel warmed, the warming itself held the reaction back, and the surge turned over.
McCardell, Herborn and Houghtaling recorded how high each surge went, how much energy it released on the way to the peak, when the peak came, and how hot the cladding of the hottest rod became. This page is about a model of the reactor fitted on all seventy, and compared with each of them in turn.
What the model did
Fitted on all seventy tests and compared with each one left out, the twin gives peak power within 6.2 percent at the median test.
The twin computes the reactor’s power, the energy it releases, and the temperatures of the fuel, the cladding and the water, through the whole surge: six groups of delayed neutrons, the transient rod’s worth over its travel, heat conducted through six rings of an average rod and of the hottest one, the feedback of the fuel and of the water, and convection to the flow. It keeps a ledger of neutrons and one of heat, and closes both at every step.
It is fitted on all seventy tests of the report: twelve numbers, nine constants of the model and the start powers of the three startup series. To see how it does on a test it was not fitted on, each test was left out in turn and the twelve numbers fitted again on the other sixty-nine. At the median test, peak power came within 6.2 percent, energy to the peak within 7.8, time to the peak within 3.0 and the rise of the hottest cladding within 10.5. Peak power was within two of the report’s standard deviations on 67 of the 70 tests.
By series, at the median: cold startup 4.2 percent on peak power, 500 °F 3.5, 260 °F 13.4 high, hot standby 15.5 low. The largest gap is the three tests from operating power, 19 megawatts: 81.8 percent low in energy and 41.7 percent early at the median, where the tests reached broad maxima timed on a hand-started clock.
Asked for the report’s cold test of one dollar at 76 °F, it gives a peak of 10.61 megawatts at 0.993 seconds with 2.17 megawatt-seconds released on the way up; test 49 of Table III, at the same dollar, measured 11 megawatts at 0.97 seconds and 2.1. Its run comes back with the proof 6db04d6b…6da155.
The first model of the same reactor, which followed the cold surges only, has a page of its own; the verifier marks it superseded by this twin. A dataset of 233 sealed runs over the seventy tests is on Hugging Face.
Comparedwith measurement
Where it stops
Compared from a cold start to operating power. Past that it keeps going and flags every step. It stops where the fuel would melt or the water boil.
In the verifier’s own words: “Past what a model was compared with, it keeps going with the same equations and flags every step. It stops only at a physical limit, or where its equations, constants or tables no longer hold, and it names the reason.”
What it was compared on
- Reactivity of 0.46 to 1.29 dollars inserted by ejecting the transient rod.
- Inlet water at 53 to 513 °F (284.8 to 540.4 K), at 0.0853 and 10.44 MPa.
- No flow up to 24 feet a second (7.32 m/s), and starting power from 4e-6 to 19 megawatts.
- Four things about each surge: peak power, energy to the peak, time to the peak and the rise of the hottest cladding, against the report’s own standard deviations.
Past that, and what its own description says of itself
- Any reactivity of zero or more, any inlet above 273.15 K and below boiling, and any pressure from 0.000611657 to 22.064 MPa, with the same equations; each step outside the compared span is flagged
FLAG_OUTSIDE_COMPARED. - A run ends where a ring of the hottest rod reaches 3120 K, the melting point of uranium oxide (
FuelMelting), or where the water in the core reaches saturation (WaterAtSaturation). - It refuses a reactivity below zero (
ReactivityNegative), a reactivity changed during a run (ReactivityChangedDuringRun), a start outside the model (StateOutsideCard) and a step above its ceiling (DtAboveStateCeiling). - It has no scram, no void feedback and no second burst.
- The startup tests give no initial power: the fitted 11.8, 4.0 and 12.5 watts are effective values for the three series.
- Fuel temperature was never measured: the cladding thermocouple is modelled as a hot rod at 1.406 times the peak-to-average power density.
For the reader who wants every number
In the verifier’s own words.
Everything above is this page’s telling. What follows is the verifier’s own, exact and whole: the spec sheet of the model energy/reactor_spert3_twin as version 0.14.3 serves it, in its six parts, with its word for how it stands against measurement: compared with measurement. The verifier’s current description is the one to trust. Where it says card it means a model, and where it says refuses it names the reason a run stops.
What it computes
Reactivity-insertion transient of the SPERT III E-core test reactor, 1392 UO2 rods, from cold startup, hot startup at 260 and 500 degF, hot standby or operating power, by six-group point kinetics with the transient rod’s worth over its travel, radial conduction in six rings of the average and the hot rod, Doppler and moderator feedback and convection to the water: power, energy released, the fuel, clad and water temperatures and the hot-spot clad temperature, with the neutron and heat ledgers closed at every step.
Range
Range: compared at 0.46 to 1.29 dollars, inlet 53 to 513 degF (284.8 to 540.4 K), 0.0853 and 10.44 MPa, no flow to 24 ft/s (7.32 m/s) and initial power 4e-6 to 19 MW; computes any reactivity of zero or more, any inlet above 273.15 K and below saturation and any pressure from 0.000611657 to 22.064 MPa with the same equations, each step outside the compared span flagged FLAG_OUTSIDE_COMPARED.
Fitted on
Fitted on all 70 tests of IDO-17281 Tables III, V and VII, every test read when the structure was chosen: twelve numbers, nine constants of the card and the start powers of the three startup series.
Compared with
Compared with each of the 70 tests left out of the fit in turn, the twelve numbers refitted on the other 69: at the median test peak power within 6.2 percent, energy to the peak within 7.8, time to the peak within 3.0 and hot-spot clad rise within 10.5; 67 of 70, 62 of 70, 43 of 66 and 61 of 69 tests within two of the report’s standard deviations.
Gap
Gap: from operating power, 19 MW, the 3 tests read 11.3 percent low in peak power, 81.8 percent low in energy and 41.7 percent early at the median; in hot standby peak power reads 15.5 percent low (test 81: 281 MW against 330), and at 260 degF 13.4 percent high.
Refuses
Refuses a reactivity below zero (ReactivityNegative) or changed during a run (ReactivityChangedDuringRun), a start outside the card (StateOutsideCard) and a step above its ceiling (DtAboveStateCeiling); a run ends where a ring of the hot rod reaches 3120 K (FuelMelting) or the core water reaches saturation (WaterAtSaturation).
Hand this one to your agent.
https://mcp.zerotrustphysics.com/mcp
Something to paste
Connect to https://
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What it will find
This model’s spec sheet: what it computes, its range, what it was fitted on, what it was compared with and how close it came, its gap and what it refuses.