Analysis basis, supplied inputs and assumptions

Process demonstration — unvalidated engineering estimates. Assumptions, transferred estimates and unresolved requirements remain explicit. This readable view does not change the source evidence.

Analysis basis means the dimensions, operating conditions, material properties, restraints and simplifications used in the calculation. Engineer approval at checkpoint A permitted this demonstration model to run; it did not validate the model or accept a physical design.

SUPPLIED values come from the original brief. ASSUMPTIONS below are analyst-selected demonstration inputs. ESTIMATES and published analogues do not establish the original 5% DNBR requirement.

Execute the complete eight-case PWR process using real reduced structural calculations and explicitly substituted thermal evidence; preserve unestablished original requirements.

Supplied requirements and operating conditions

Quantity	Value	Origin
Rod outside diameter (mm)	9.5	Supplied brief
Rod pitch (mm)	12.6	Supplied brief
Nominal wall-to-wall gap (mm)	3.1	Supplied brief
Rod array	5 × 5	Supplied brief
Coolant pressure (MPa)	15.5	Supplied brief
Inlet temperature (°C)	290	Supplied brief
Mass flux (kg/(m²·s))	3000	Supplied brief
Bowed-rod linear heat rate (kW/m)	25	Supplied brief
Effective support stiffness (N/mm)	50; 20	Supplied brief
Cladding material	Zircaloy-4	Supplied brief
Requested gap closure	50%, 80%, 100%	Supplied brief
Reference gap closure	0%	Added comparison baseline
Maximum DNBR penalty	5%	Supplied comparison criterion; NOT established

ASSUMPTIONS — reduced structural model

Quantity	Value	Status
Span	1000 mm	Assumed
Cladding wall	0.57 mm	Assumed
Elastic modulus	77420.038 MPa	Provisional sourced property
Poisson ratio	0.383780	Provisional sourced property
Fresh / irradiated spring stiffness	50 / 20 N/mm	Supplied values; single effective spring is an assumption
Spring preload	0 N	Assumed for incremental calculation
Closure cases	0%, 50%, 80%, 100%	0% baseline added; others supplied

Structural method and applicability

Item	Definition or value
Analysis idealization	One initially straight, homogeneous hollow pipe beam; the neighbor is a geometric reference only. The 25-rod SteveCAD model is retained context, not the finite-element mesh.
Finite element and mesh	B32R, native PIPE section; 100 elements, with 50/200-element pilot comparisons
End restraints	Pinned lateral ends; axial datum at first end, free axial motion at other end; planar y displacement restrained, one torsional datum. Bending rotations remain free.
Spacer-grid representation	A single bilateral, zero-preload incremental SPRINGA at z=500 mm represents aggregate transverse stiffness. It does not resolve individual springs/dimples, separation or strap clearance.
Applied deformation	Prescribed x displacement at z=500 mm produces nominal 0/50/80/100% midplane closure against an undeformed neighbor. The actual nodal maximum and gap are checked independently.
Elastic property source	Previously retained Zircaloy-4 zero-cold-work/zero-fluence card at 573.15 K; no new material correlation.
What the calculation represents	A forced-displacement sensitivity calculation, not an irradiation-induced natural-bow prediction. Grid displacement equals closure only because this reduced model explicitly imposes that arrangement.
Interpretation of stiffness comparison	At the same imposed midpoint displacement, changing a colocated grid spring changes reaction but should not change the elastic beam deformation or bending stress. Report this as a model consequence.
Interpretation of 100% closure	100% is geometric touching at the nominal midplane; contact pressure and additional contact load remain not established.
Stress reporting location	Use actual global axial stresses at native integration points and paired zero-closure subtraction. These are not an outer-surface peak or a local contact stress.
Effects excluded	rod-to-rod contact and load redistribution; grid strap interference; spring/dimple travel/yield; local cladding contact stress; coolant/internal-pressure stresses; pellet interaction; creep and irradiation constitutive response; thermal gradients

SUBSTITUTED THERMAL EVIDENCE — applicability limits

Item	Definition or value
Classification	Published experimental/simulation reference and unvalidated transferred estimate
Native reuse	Reuse exact completed CoolProp states and conditional bulk heat balance for identical input assumptions; no repeated property calls.
Bulk assumptions	63 mm square enclosure; all 25 rods at 25 kW/m; 0.5/1/1.5 m lengths; constant 15.5 MPa; steady adiabatic global balance. Only the bowed-rod power was supplied.
Mapping	0: 166; 50: 170; 80: 169; 100: 167; 168
Transfer	HTRF 85% closure is a disclosed proxy for 80%. Preserve all source P/T/G and geometry differences. Report both contact arrangements separately.
Derived quantity	Published CHF divided by the assumed study mean heat flux may be shown only as an illustrative reference scaling index, never as study DNBR.
Stiffness	Reuse identical thermal references for both stiffness states; no invented stiffness-to-CHF multiplier.
Uncertainty	Spread of selected source rows and declared sensitivity cases; not a confidence interval or demonstrated conservative bound.
Unavailable	local flow redistribution; wall-temperature field; rod-to-rod heat transfer; study CHF; study DNBR; 5% DNBR compliance

ESTIMATE — end-of-life reference transfer

Item	Definition or value
Classification	Unvalidated transferred estimate
Source	Retained X-750 plate aged 977 K for 24 h; NRU reference around 570–573 K, fluence 6e24 n/m2.
Retention	0.5021626
Assumed fresh preload n	5
Conditional eol preload n	2.510813
Separation	This retained material/history-specific transfer estimate is reported separately; it is not the 20/50 stiffness ratio and is not included as a preload in the zero-preload incremental beam model.

Numerical verification plan

Item	Definition or value
Scope	Numerical execution and demonstration consistency only; no physical acceptance.
Required	All eight case identities and exact deck hashes; Native completion and finite U/RF/S; Actual midpoint displacement and nodal minimum gap; Global x-force balance including anchor and prescribed-motion reactions; Grid anchor reaction against the configured native linear spring relation; Paired baseline subtraction at identical integration-point identities; Three-level pilot comparison of bending stress and reaction; Labels, source conditions and original DNBR status retained
Tolerances	Displacement mm: 1e-05; Force balance relative: 0.001; Force absolute n: 0.0001; Spring reaction relative: 0.001; Pilot refinement relative: 0.05
Missing behavior	Preserve failed result; hold B or result verification. Never fill missing native observations with predicted values.

Source record and traceability

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Presentation generated from this retained record. Historical status fields describe the source revision; later review decisions are explained on the engineering review page.