The validation record

The catalogue holds 47 cases. Each states what was compared, against what, the agreement found and what that agreement shows, and each is tiered by what its evidence is.

What a tier says

A measurement on an operating plant or a controlled rig is evidence of how far the model is from the plant. A textbook worked example is a published calculation: reproducing it shows that the method is implemented as published, and says nothing of how close the method is to a plant. A comparison with CFD, a co-simulation or another model is a comparison of two models of one plant and validates neither.

A measurement whose source states no uncertainty is used at the weight of a comparison with another model. The uncertainty band on a result covers the uncertainty of its equations; a model-form uncertainty rests only on measured plants with a stated uncertainty.

Tier 1: measurement on an operating plant; 2
Tier 2: measurement on a controlled rig; 13
Tier T: a textbook worked example - a published answer, not a measurement; 13
Tier 3: CFD, co-simulation or another model; 19

Measurements on operating plants

Table 1. The 2 cases at Tier 1: the case, the system or rig it was run on, and the agreement found.
Case	System	Agreement
Kendal under crosswind: the printed method against a full-scale plant, and against its own author's model Used at Tier 3: its source states no uncertainty.	Indirect dry cooling, natural draft, horizontal array	As printed, the model over-predicts the measured rise by a factor of 1.75 at 4 m/s, 1.45 at 6 m/s and 1.71 at 8 m/s.
ASME PTC 30.1 Appendix A: the field test against the reconstructed plant	Air-cooled condenser, A-frame forced draft	The measured flow is 105.0 to 106.5% of the prediction, 106.1% over the four hours.

Measurements on controlled rigs

Table 2. The 13 cases at Tier 2: the case, the system or rig it was run on, and the agreement found.
Case	System	Agreement
Dong et al. 2021The Gatton tower's start-up from cold	Indirect dry cooling, natural draft, horizontal array	The water temperature is within 0.2 K of the measurement at 200 s, and the first plume reaches the top of the tower at 225 s against about 280 s measured.
Dong et al. 2021The Gatton tower's steady end-state, from a second campaign	Indirect dry cooling, natural draft, horizontal array	The model over-predicts the heat transfer rate by 25.8% with its default air-side relations and by 12.3% with the paper's own bundle loss coefficient, both far outside the measurement uncertainty.
Gatton 20 m NDDCT: the best system case in the library, and why it still cannot carry model-form uncertainty	Indirect dry cooling, natural draft, horizontal array	On the default air-side relations the model over-predicts the heat transfer rate by 17.9% and the air mass flow rate by 19.2% on average, while the air temperature rise is within 1.1%, so the error lies in the draft.
Taylor 2004Four plain plate-fin water coils in a wind tunnel, against Wang et al. (2000)	A finned-tube bundle on a rig	Wang's relations deviate from the measurements by 8.4% on the Colburn factor and 11.1% on the friction factor, averaged over the four coils, and Taylor's own comparison (Table 6.3) is reproduced to within two points on the Colburn factor.
Wei's wind tunnel on a Heller ring: the pressure coefficients want 0.62, the heat-side correction wants nothing Used at Tier 3: its source states no uncertainty.	Indirect dry cooling, natural draft, vertical bundles	As printed, Kröger's crosswind method over-predicts the loss three- to fourfold: C_w is −20% at a velocity ratio of 2 and −30% at 3.2, against the measured −5.0% and −8.9%.
Briggs & Young against an independent annular finned tube bundle	A finned-tube bundle on a rig	The correlation is 1.0 to 6.4% above the measured fit, highest at the bottom of the Reynolds number range, and every point lies within the case's tolerance of 6.8%, the reference's measurement uncertainty and fit deviation combined.
Ganguli against the same bundle, and why it is no longer the default	A finned-tube bundle on a rig	Ganguli's relation over-predicts the coefficient by +20.0% at Re 4813, rising to +41.6% at Re 1176, and every point fails the case's tolerance of 6.8%.
Kröger Eq. 5.5.9 against Wu's measured friction factor	A finned-tube bundle on a rig	Eq. 5.5.9 agrees with the measured fit to within -4.3% to +1.1% across the whole range, with a mean absolute deviation of 2.8%.
The Monju plant relation against Wu's rig, in the regime both were measured in	A finned-tube bundle on a rig	The Monju relation lies within −1.0% to +4.1% of the fit, every point inside the case's tolerance of 6.2%.
What extrapolating Robinson & Briggs costs, measured	A finned-tube bundle on a rig	The relation reads 22.0% low at Re 4813 and 42.3% low at Re 1176, worsening monotonically as the Reynolds number falls.
NCEPU wave-finned flat tube: the air-side fit against its own wind tunnel	Air-cooled condenser, A-frame forced draft	Four of the ten points, at face velocities of 1.93 to 3.34 m/s, lie within the 7% tolerance.
Wang's plain-fin relations against Zhu's small-tube plate-fin air cooler	A finned-tube bundle on a rig	Wang's Nusselt number is 18.5 to 44.4% above the measured fit (30.9% on average), the excess falling with the Reynolds number, and Wang's friction factor is 21.6 to 26.5% below it (24.6% on average).
Shah's condensation correlation against Zhu's inclined small-tube air-cooler rig	A condensing tube on a rig	Regime I lies within 30% of the measurement at all 30 points and below it at every one, from −4.8% at the top of the range to −28.9% at the bottom, with a mean absolute deviation of 17.3%.

Textbook worked examples

Table 3. The 13 cases at Tier T: the case, the system or rig it was run on, and the agreement found.
Case	System	Agreement
Kröger Example 7.3.1 closed on its own heat transfer rate: the loop returns his water temperature	Indirect dry cooling, natural draft, horizontal array	The loop returns a water inlet temperature of 334.59 K against the example's 334.60 K (61.45 °C), a difference of 0.01 K, within the case's tolerance of ±0.05%.
Kröger Example 7.3.1Indirect natural-draft tower, horizontal array	Indirect dry cooling, natural draft, horizontal array	The heat transfer rate is reproduced to within 0.024% and the air mass flow rate to within 0.010%, and both outlet temperatures to within 0.005 K.
Kröger Example 8.1.1Forced-draft air-cooled heat exchanger bay	Air-cooled heat exchanger, forced draft	The air mass flow rate is reproduced to within 0.10%, the heat transfer rate and the fan shaft power to within 0.04%, and every temperature to within 0.04 K.
Kröger Example 8.1.2Induced-draft air-cooled heat exchanger bay	Air-cooled heat exchanger, induced draft	The air mass flow rate is reproduced to within 0.10%, the heat transfer rate and the fan shaft power to within 0.04%, and every temperature to within 0.04 K.
Kröger Example 8.1.4A-frame air-cooled steam condenser	Air-cooled condenser, A-frame forced draft	The air mass flow rate, the heat transfer rate and the fan power are reproduced to within 0.011%, and every published loss coefficient to five significant figures.
Kröger Example 8.3.1A forced-draft bank of six bays	Air-cooled heat exchanger, forced draft	The heat transfer rate of the bank on Kröger's flow-proportional arithmetic is reproduced to −0.039% of his 73.739 MW, and the inlet flow ratio of 0.985 within the case's tolerance of ±0.5%.
Kröger Examples 8.3.2 and 8.4.2An eighteen-unit air-cooled condenser bank	Air-cooled condenser, A-frame forced draft	The inlet flow ratio of 0.98398 and the bank's plan width and length are reproduced exactly, and the bank's flow-proportional heat transfer rate of 347.68 MW to 0.004%.
Kröger Example 8.4.1Plume recirculation on a forced-draft bank	Air-cooled heat exchanger, forced draft	The recirculation effectiveness of 0.9924 is reproduced to within 0.004%, and the inlet flow ratio of 0.985 lies within the case's tolerance of ±0.5%.
Kröger Example 9.2.1The same tower with its A-frames laid flat	Indirect dry cooling, natural draft, horizontal array	The heat transfer rate is reproduced to within 0.90% (351.2 MW against 354.39 MW) and the water outlet temperature to within 0.055% (0.17 K), with nothing tuned.
Kröger Example 9.2.2The horizontal array under a 6 m/s crosswind	Indirect dry cooling, natural draft, horizontal array	The water inlet temperature is reproduced to within 0.11 K (+0.033%), the water and mixed air outlet temperatures to within 0.035%, and the air mass flow rate to within 0.26%.
Kröger Example 9.3.1The six-bay bank under a 3 m/s crosswind	Air-cooled heat exchanger, forced draft	The model gives a mean fan flow ratio of 0.917 against Kröger's 0.9 and a recirculation effectiveness of 0.967 against his 0.97, and the heat transfer rate of the bank comes out 1.5% above his 65.355 MW.
Kröger Example 9.3.2The six-bay bank under a 3 m/s wind along its axis	Air-cooled heat exchanger, forced draft	The heat transfer rate of the bank is reproduced to 0.5% below Kröger's 67.546 MW, which is the rounding of his own curve readings, and the recirculating fraction is read as 0.067 against his 0.065.
NDDCS design pointDirect natural-draft tower, vertical bundles	Direct natural draft, vertical bundles	The heat transfer rate is 0.48% above the published value (923.3 MW against 918.9 MW) and the air mass flow rate 3.5% above it (45 545 kg/s against 44 016 kg/s), both within the case's tolerance of 5%.

CFD, co-simulation and other models

Table 4. The 19 cases at Tier 3: the case, the system or rig it was run on, and the agreement found.
Case	System	Agreement
Induced-draft A-frame condenser: a regression pin with no published answer	Air-cooled condenser, A-frame induced draft	No agreement with an independent source is claimed.
Bekker et al. 2022A 20-fan induced-draft ACC bank, against the section 8.3 and 8.4 correlations	Air-cooled condenser, A-frame induced draft	Kröger's recirculation correlation (Eq. 8.4.25) gives 0.99126 against the study's 0.990, +0.13%.
Bekker et al. 2022The induced-draft bank under wind, along and across its axis	Air-cooled condenser, A-frame induced draft	Every published row is reproduced within the case's tolerance of ±0.5%.
Carrier 28B Nu-Fin coils (2007): catalogue heating capacities and dry friction against the plate-fin chain	Dry cooler, plate-fin coil	On the tube layout the printed water balance supports, the heating capacity lies between −11.8% and +19.8% of the catalogue (mean +8.9%); on the other layout it lies between −27.4% and −3.2% (mean −13.3%).
He et al. 2013A 112-cell air-cooled condenser under crosswind to 12 m/s: the extrapolation's size	Air-cooled condenser, A-frame forced draft	At 2 m/s the whole-condenser flow ratio agrees to within 0.2 points (0.982 against 0.98).
He et al. 2013A 2 × 600 MW air-cooled condenser, windless: the first large-ACC steady comparison	Air-cooled condenser, A-frame forced draft	Given the plant's steam flow, the back pressure is 26.08 kPa against 26.8 kPa (−2.7%).
Kong's conventional indirect ring under crosswind: the air flow of an indirect ring wants the same k = 0.5	Indirect dry cooling, natural draft, vertical bundles	Windless, the air mass flow rate is 47 492 kg/s against 49 668 kg/s (−4.4%).
Kong's annular (180°) NDDCS against its own CFD	Direct natural draft, vertical bundles	The air mass flow rate is reproduced to −3.82% and the heat transfer rate to −1.93%.
Kong's apex sweep: the apex trend is not a settled reference, and the model sits between two of them	Direct natural draft, vertical bundles	The two references disagree by a factor of 2.3, +10.39% and +24.37% from 60° to 180°, and the model lies between them at +12.81% to +16.21%.
Kröger's crosswind method on Kong's two delta rings, 3 to 15 m/s	Direct natural draft, vertical bundles	As printed, the method over-predicts the effect of wind about twofold: the model's Q/Q₀ lies 8.9 and 5.8 points below the CFD's at 6 m/s on the two rings, and 23.1 and 16.9 points below at 15 m/s.
Kong's triangular (60°) NDDCS against its own CFD	Direct natural draft, vertical bundles	The air mass flow rate is 2.82% above the CFD (33 509 kg/s against 32 590 kg/s) and the heat transfer rate 5.97% above it (1 205 MW against 1 137 MW).
Liu's one-tower 2 x 660 MW plant under crosswind: the largest ring, a held load, and a sixth air-flow multiplier	Direct natural draft, vertical bundles	Windless, the air mass flow rate is 4.7% below the CFD with two units and 6.1% above it with one.
ASME PTC 30.1 Appendix A: the reconstructed plant against the vendor's curves	Air-cooled condenser, A-frame forced draft	Over the forty points the model's pressure is 1.5% above the vendor's on average, 3.6% root-mean-square and 6.5% at worst.
ASME PTC 30.1 Appendix K: a 35-cell ACC's fans under a 5 m/s wind	Air-cooled condenser, A-frame forced draft	The model's unit flow under the wind is 0.978 of its still-air flow against the CFD's 0.78, 20 points milder; its upwind column is 0.81 against 0.506, its interior stays at the still-air ratio against 0.828, and its downwind column is 1.08 against 0.912.
Strydom et al. (2026) co-simulationIslanding scenario	Direct natural draft, vertical bundles	The back pressure peaks at 49.3 kPa at about 26 s against the co-simulation's 74.7 kPa at 43 s, 34% low and earlier, and the run settles in 85 s against 140 s.
Strydom et al. (2026) co-simulationStep scenario	Direct natural draft, vertical bundles	Under the co-simulation's own conditions and with no parameter fitted, the back pressure peaks at 146.8 kPa at 891 s against 142.2 kPa at 850 s, the wall at 383.8 K against 382.9 K, and the air mass flow rate reaches 1 500 kg/s at 969 s against 1 050 s.
Indirect natural-draft tower with vertical bundles, against an independent implementation	Indirect dry cooling, natural draft, vertical bundles	The air mass flow rate is reproduced to within 0.7% (11 573 kg/s against 11 492 kg/s) and the heat transfer rate to within 0.2% (351.2 MW against 352 MW), inside the case's tolerance of ±1.5%.
Yang et al. 2012Two 56-cell air-cooled condensers under wind from five directions: what the direction rule can and cannot carry	Air-cooled condenser, A-frame forced draft	The model does not reproduce the study.
Zhao's Heller tower under crosswind at constant loadA third family, and a third multiplier	Indirect dry cooling, natural draft, vertical bundles	The model under-predicts the rise by 2.2 to 3.2 K up to 8 m/s, about a quarter of a 5 to 12 K rise, comes within 0.3 to 1.2 K at 12 and 16 m/s, and over-predicts by 1.7 K at 20 m/s, where the CFD recovers.