CelerisLab/docs/validation/duetsch_re100_kc5_protocol.md

Prescribed in-line oscillation: Dütsch Re 100 / KC 5 — PROTOCOL (review draft)

Production under test: claude/moving-bodies-s3a at 653fd997 (unchanged). Primary source: Dütsch, Durst, Becker & Lienhart, J. Fluid Mech. 360, 249–271 (1998), doi:10.1017/S002211209800860X. Source facts below were verified from the paper (Slack C0C78UFKGRM/1793335557.460509, TRON 1793356317–1793356724, page numbers given). Everything marked ENGINEERING is our a-priori choice, fixed before any benchmark result; it is not a paper uncertainty.

0. Source facts (with provenance)

• Motion (p.251): x_c = -A sin(2 pi f t); paper phase phi = 0 is the mean position moving left at -U_max. KC = 5 gives A/D = 5/(2 pi) = .7957747.
• Start (p.254): the computation starts a quarter cycle before phi = 0, at x = +A with zero velocity (phi = -90°).
• Experiment (pp.252, 254–256): D = 10 mm, L = .65 m, tank 1.2 × .7 × .7 m, rho = 998.2 kg/m³, mu = 1.00818 mPa·s, Re = 100, KC = 5; LDA with 1° phase bins and 200 samples per node and degree; no quantified experimental error recovered.
• Profiles (Fig. 8, p.260): LAB-FIXED stations x1 = -6, 0, 6, 12 mm, i.e. x/D = -.6, 0, .6, 1.2, at phi = 180°, 210°, 330°; u1 and u2 versus x2.
• Original numerics (§2): cylinder-fixed accelerated frame (x_i = x~_i + x_i,s, outer velocity -u_c, inertial source -rho du_c/dt), O-grid outer diameter 120 D, illustrated 192 circumferential nodes, 720 steps/cycle; tank influence neglected.
• Force fit (verified): force ON THE BODY per unit span F1 = -0.5 rho D c_d xdot|xdot| - (pi/4) rho D² c_i xddot with x = -A sin phi; normalized by 0.5 rho D U_max²: c_d cos phi |cos phi| - (pi² c_i / KC) sin phi. c_i is the ADDED-MASS coefficient; total inertia c_m = c_i + 1 is a different convention and is not used.
• Table 1 computed Morison coefficients (c_d, c_i) for 96 / 192 / 384 perimeter nodes at dt/T = 1/720: (2.15, 1.42), (2.10, 1.45), (2.09, 1.45). These are fitted computed coefficients, not a measured force and not an error bar. The paper states the coarse direct force is closer to the finest direct force than the Morison fit, but gives no waveform-error norm.

1. Kinematics, time levels and phase bookkeeping

• Our run is in the LAB frame: the circle moves, the fluid is initially at rest (rho = 1, u = 0); no fictitious inertial source is added. Lab-fixed profile stations are compared directly (no frame transform needed).
• Geometry reference: the circle's base centre is the INITIAL position, the right turning point x_mean + A; the declared offset box is x in [-2A, 0], y = 0. The body is never teleported: offset 0 at s = 0.
• Elapsed time s = n dt from the start. Analytic position relative to the mean x(s) = A cos(2 pi s / T), velocity u(s) = -U_max sin(2 pi s / T); paper phase phi = (360 s / T - 90) mod 360.
• Step n moves from s_n to s_{n+1}: target offset x(s_{n+1}) - A; wall velocity = the single-step interval average (x(s_{n+1}) - x(s_n)) / dt (analytic, supplied, not differenced from stored offsets). The per-step force of run(1) / read_force(normalize=True) is attributed to that same interval.
• Paper cycle k = 1, 2, ... spans s in [T/4 + (k-1) T, T/4 + k T); the initial quarter cycle (s < T/4) is cycle 0 and never scored. Every logged sample carries (k, phi). Example: phi = 330° of cycle 1 is at s = 7T/6.
• T is chosen as a multiple of 360 native steps, so phi = 180°, 210°, 330° fall exactly on step boundaries and 1° bins hold whole steps.

2. Resolution ladder (uniform grid, fixed Mach), ENGINEERING

D (cells)	T (steps)	U_max = 5 D / T	nu_lat = U_max D / 100	tau (3 nu + .5)
20	2,520	.039683	.0079365	.5238
40	5,040	.039683	.015873	.5476
80	10,080	.039683	.031746	.5952

• MRT collision. Mach fixed (Ma ≈ .0687); a separate Mach check at D = 40 with T = 10,080 (U_max halved, tau .5238) is labelled MACH and not part of the ladder.
• Per-step displacement ≤ U_max ≈ .04 cells (bound .5).

3. Domain and boundaries (finite-domain reproduction), ENGINEERING

• Boundary family (runner owner confirms the zero-velocity inlet is supported as configured before any run): the native dense channel only — zero-velocity inlet, pressure-NEQ outlet, y walls (bounce-back). This is a finite-domain approximation of the paper's 120 D O-grid, NOT infinite still fluid. The G4 periodic/slip overrides are a different family and are not substituted.
• Sensitivity order (each step at D = 40 before the ladder is run):
  1. box 24 D × 24 D vs 48 D × 48 D (cylinder mean position at the centre);
  2. the larger box is accepted if section 6 domain criteria pass between the two; otherwise 96 D is tried once (memory/runtime measured first); if that still fails, the domain verdict is FAIL and is reported.
• The ladder (D = 20 / 80) uses the accepted box size in units of D.
• Memory/runtime: measured by a smoke run before each new size; measurements inform scheduling only, never tolerances.

4. Observables (raw, per step, preserved)

• obs Fx, Fy (CME) and all MovingTables.DIAG columns per step: CME, CME + Wen and CME + cover − uncover reported separately; crossings, eq_only, no_donor (no_donor must stay 0).
• Velocity u1, u2 on lab-fixed lines x/D = -.6, 0, .6, 1.2 (relative to the mean cylinder position) versus x2, at every step of the scored phases.
• Interpolation: bilinear on cell centres using only cells that are fluid at that step (flags read back via get_flags()); weights renormalized over the fluid corners; a sample with no fluid corner, or inside the circle at that step, is MISSING and logged, never set to zero. One-degree bins carry only valid samples.

5. Periodic-regime gate (every case, before any statistic)

Ledger rows, same schema for every case:

field	content
dx, dt	in D and in T units
U_max, nu, Re, KC	lattice and nondimensional
T	native steps and nondimensional time
duration	native steps, s/T, number of paper cycles
discard	cycle 0 plus all cycles before the accepted window
window	the common accepted window (below)
cycle ledger	per cycle k: phase-aligned waveform change and profile change (below)
verdict	PASS or FAIL-CLOSED

• Settling metric, ENGINEERING, fixed scales (no near-zero denominators):
  • force: max over phase of |F_k(phi) - F_{k-1}(phi)| / (0.5 rho U_max² D) on the per-step CME waveform aligned by step index within the cycle;
  • profiles: max over scored stations/phases/points of |u_k - u_{k-1}| / U_max.
• Rule: K_case = the smallest cycle k ≥ 4 for which both metrics are ≤ .005 for the N = 3 consecutive pairs (k-3→k-2), (k-2→k-1), (k-1→k).
• Cap: 30 paper cycles per case; not settled by the cap → FAIL-CLOSED.
• Common window: K = max over all compared cases of K_case; every case is run to cycle K + 2 and scored on cycles K, K + 1, K + 2 (same indices).
• FAIL-CLOSED also if any case covers fewer paper cycles than K + 2, if windows differ, or if the ledger is missing.
• The earlier G4 timing check (100 coarse vs 400 diffusive-fine steps) was a matched short transient, not periodic evidence.

6. Metrics and per-observable criteria (ENGINEERING, not paper uncertainty)

• Morison fit: least squares of the normalized per-step force over the accepted window against the two basis functions above, each averaged over its single step interval, fixed paper phase, no free phase shift; outputs c_d and added-mass c_i per force candidate.
• Criteria:
  • cross-resolution: for each observable, the D20→D40→D80 differences to D80 must decrease; force waveform: normalized RMS difference D40 vs D80 ≤ .02 (scale 0.5 rho U_max² D); profiles: RMS D40 vs D80 ≤ .02 U_max;
  • domain (section 3): same two norms ≤ .01 between the two box sizes;
  • against Table 1 (computed reference): |c_d - 2.09| ≤ .06 and |c_i - 1.45| ≤ .04 at D = 80 (our engineering bands; the table's own 96→384 change is reported alongside, not used as an error bar);
  • against Fig. 8 LDA: QUALITATIVE ONLY. The original figure could not be accessed or rendered (TRON 2026-10-30); no digitized ordinates and no measurement uncertainty exist. No quantitative profile pass is claimed. A quantitative criterion may be declared only after an accessible original figure or data set and a documented digitization (figure, tool, uncertainty) exist, and before that comparison is run.
• No force candidate is selected for an RHS by these results; each is reported.

7. Order and scope

Protocol review → lean test driver (no production change; reuses the existing Simulation API) → smoke (memory/runtime) → domain sensitivity → ladder → physical-validation verdict → only then single-cylinder VIV. No AMR, no pinball, no manuscript work.