# Power-piping research cases · v1.3

Four service families provide reusable **solid-FE component operators**, rather
than attaching service names to the old small-pipe library. Each family has
three straight lengths (3D, 5D, 8D) and three 90° bends (R/D = 1.5, 2, 3).
Each bend also contains a 2D tangent at both ends. Layouts are researcher-designed.

| Research family | OD × wall / mm | E / GPa | α / µm/(m·K) | Example ΔT / K |
|---|---:|---:|---:|---:|
| Main steam / 主蒸汽 | 450 × 60 | 170 | 13 | 546 |
| Hot reheat / 再热热段 | 800 × 30 | 170 | 13 | 546 |
| Cold reheat / 再热冷段 | 800 × 20 | 190 | 12.5 | 330 |
| High-pressure feedwater / 高压给水 | 450 × 50 | 195 | 12.5 | 280 |

## Provenance and assumptions

The **main-steam cross-section only** derives from Gao & Huo, *Feasibility
Research on Ultra-supercritical 350 MW Unit and Analysis of Main Equipment
Parameter*, Table 9: 330 mm bore and 60 mm calculated wall, excluding corrosion
allowance. The derived OD is 450 mm. It is not a purchased/as-built pipe size.
Source: https://doi.org/10.16516/j.gedi.issn2095-8676.2019.04.007

The other three cross-sections are **author-selected benchmark geometries**.
All tabled effective E and α values, temperature rises, layouts, springs,
damper settings and forces are **benchmark assumptions**, not values extracted
from that paper, certified grade-specific material data, or measured plant data.
Density is 7850 kg/m³ and Poisson ratio 0.3. ΔT is a uniform imposed wall
temperature rise, not an absolute operating temperature or a transient history.
Material constants remain fixed when ΔT is varied.

The service taxonomy follows main steam, hot reheat, cold reheat and main
feedwater. Context: National Energy Administration,
https://www.nea.gov.cn/2011-02/14/c_131071160.htm

## Models and records

- 24 new components, 35,280 displacement DOFs each; Q2 displacement on a Q1
  hexahedral geometry, 24 axial × 24 circumferential × 2 radial cells.
- 12 rigid mechanical port DOFs plus 12 fixed-interface modes per component.
- 108 assembly records: four families × three layouts × three support choices
  × three temperature rises. Labels come from the assembled component ROM.
- 12 harmonic sweeps: four families × three support choices, with a 1000 N
  peak Y force at the final joint, assumed 2% modal damping, and a 10,000 N·s/m
  grounded Y damper at that same joint. Their excitation frequency is f1.
- UI initial layouts use springs at joints 3 and 5; they are editable examples,
  not identical to every dataset layout or an optimized support design.
- Original 48 components and 512 assembly records remain intact.

Mass and unconstrained axial expansion are checked analytically. Python/SciPy
and browser assembly are compared for all 108 records. Harmonic response is
checked against an independent complex solve, including 12/24 system-mode
retention. Four R/D=3 bends are compared against 30 × 32 × 3 meshes (81,984
DOFs). The refinement check covers isolated bends, not every route, stress,
or higher mode. Reports state each metric explicitly.

## Scope

These are dry-pipe, small-displacement linear elastic models. No pressure
stiffening, fluid/insulation mass, spring preload, gaps/friction, creep, fatigue,
thermal gradients or piping-code acceptance calculation is included. A viscous
damper is not a hydraulic snubber. Displayed response is centreline motion, not
wall stress. This release supports reproducible geometry/support studies and
operator reuse; it is not a plant digital-twin calibration or design sign-off.

## Reproduce

In the downloaded dataset repository, first run:

```sh
mkdir -p data reports
ln -s ../components data/components
ln -s ../assemblies data/assemblies
ln -s ../dynamics data/dynamics
```

These relative links recreate the development layout without copying matrices.
Skip a link if it already exists. With AgentFEM/DOLFINx, run
`python source/validate_power.py` and `python source/check_power_mesh.py`.
To regenerate component operators, run `python source/generate_power.py`;
existing components are reused, so use a separate workspace for a clean rebuild.
With Node.js: `node source/check_power.cjs`.
With NumPy/SciPy: `python source/check_power_harmonic.py`.
For a compact model-only example, run `node example_power.cjs` from the
downloaded model repository. No solid-FE environment is needed for that example.
The data/model repositories include the required operator data and source;
the Space contains only compact browser operators and needs no Python backend.

## 中文说明

本版增加的是可复用、可验证的四大管道研究组件。主蒸汽截面有公开计算尺寸
来源；其他截面和工况为研究设定。先研究管路走向、支撑位置和刚度对热位移、
接口载荷与振动的影响，不将结果用作现场管道的安全判定。