92 lines
5.2 KiB
Markdown
92 lines
5.2 KiB
Markdown
# Single-cylinder free transverse VIV — PREDECLARATION DRAFT (not frozen)
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Stage goal (Yanqi via TRON): prescribed Dütsch case + one VIV case both
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"reasonably close" to a predeclared reference = development-stage success, then
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cleanup. The frozen Dütsch settling failure (0/28 pairs at 31.25 T) stays on
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record. Practical closeness is not a formal validation claim. No code until
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this page is jointly agreed.
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## Primary case (one case)
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- Reference: Qin et al., arXiv:2003.12186, §4.5 (maximum amplitudes at
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U_red = 3…8: .075, .551, .520, .459, .370, .084 D in the text, as quoted by
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Grok/Astra) for the target; setup from Kolahdouz et al., arXiv:2003.12046,
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§4.1.1 (read 2026-10-30 via ar5iv): U* sweep 3–8 with amplitudes only in
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Fig. 3(b) (no text values), domain [−30, 45] D × [−30, 30] D with the
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cylinder "initially at rest and centered at the origin", uniform inflow on
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the left, zero normal traction and tangential velocity at the outlet, zero
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normal velocity and tangential traction on y = ±30 D; no initial
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perturbation and no total simulated time stated.
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- Re = 150, U* = U/(f_n D) = 5, m/(rho D²) = 2 (m* = rho_s/rho_f = 8/pi),
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zeta = 0, f_n = sqrt(K/M)/(2 pi) in vacuum. Transverse DOF only.
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- Target: A_max = .520 D (peak amplitude, Qin §4.5). Multi-code reference
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(Kolahdouz ILE-NS, Qin II-LBM). Reference uncertainty: not stated; the
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spread between codes is not quantified here.
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## Our reproduction (declared differences)
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- D = 40, MRT, dense double buffer; U_lat = .04, nu = U D / 150 = .010667,
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tau = .532.
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- Box 75 D × 60 D (3000 × 2400) with the cylinder 30 D from the inlet, 45 D
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from the outlet, centred in y (Kolahdouz §4.1.1).
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- Boundaries: uniform Zou–He inlet, NEQ outlet (rho = 1, backflow clamp),
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free-slip y walls. Kolahdouz uses a traction outlet: declared mismatch.
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- Qin's own VIV box (40 D × 20 D) is not used; a smaller box would be a
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declared cost cut with more blockage, not "the same case".
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- Allowed y offset ±1.5 D; peak transverse speed ≈ .026 cells/step (bound .5).
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## Structure, coupling and time levels
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- M = 2 rho D² (lattice rho = 1), f_n = U/(5 D) = 2e-4 per step, K = M (2 pi f_n)²,
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zeta = 0. Equation of motion uses the structural mass only.
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- Time levels (binding): the target y^{n+1} must be set before step n runs
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(`set_body`, then `run(1)`), so step n moves the body with (y^n, v^n) that
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were advanced using F^{n-1} from the previous fluid step; step n measures
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F^n. One step of explicit lag, declared.
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- Structural update over one step with constant force F = F^{n-1} (exact
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harmonic solution, zeta = 0): y_e = F/K, w = 2 pi f_n,
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y^{n+1} = y_e + (y^n − y_e) cos w + (v^n / w) sin w,
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v^{n+1} = −(y^n − y_e) w sin w + v^n cos w.
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- Primary RHS (single coupled run): CME + Wen (theory-motivated stage choice:
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Galilean-invariant link correction; G4 could not separate it from CME).
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Raw CME and the node terms are logged as diagnostics of that trajectory;
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the node impulse is not added. A run with CME-only as RHS is a separate,
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labelled sensitivity case, decided separately. Neither RHS is claimed proven.
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## Window, failure semantics, acceptance (engineering, development stage)
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- Start: fluid at rest at U = 0 except the uniform inlet (impulsive start as
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in the reference), body at rest. The reference states no perturbation; a
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numerically symmetric start can delay or suppress lift, so one declared
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seed is used: initial structural displacement y0 = +.05 D (2 cells) with
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v0 = 0, released at t = 0. No other perturbation; not changed afterwards.
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- Response cycles: delimited by consecutive upward zero crossings of y about
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its running mean; per-cycle peak = max |y − mean| in that cycle.
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- Settled when the per-cycle peak changes ≤ 2 % between consecutive 10-cycle
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windows and the last 5 cycle peaks agree within 1 %. The 20 scoring cycles
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follow settling and are included in the cap of 150 response cycles from
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t = 0 (about 150 × 5,000 = 750,000 steps, t U/D ≈ 750); total steps and
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t U/D are reported.
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- Growth transient vs instability: amplitude growth from the seed that stays
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below 1.0 D (about twice the largest reference peak, .551 D) is a physical
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transient and is not a failure by itself. Instability = |y| > 1.0 D, a
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non-finite value, or the offset box being reached.
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- FAIL-CLOSED and reported (no sub-iteration, no RHS or parameter retune):
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unsettled at the cap, instability as defined above (possible weak-coupling
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instability at m* ≈ 2.55), or no_donor > 0.
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- Score over the 20 cycles after settling: A_max/D (mean of cycle peaks) and
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f/f_n (reported; no target).
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- Acceptance: |A_max − .520 D| ≤ .052 D (±10 %), stated together with the
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boundary mismatch and the absence of a quoted reference uncertainty. A pass
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is "reasonably close" for the stage: not grid convergence, not force-RHS
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validation, and it does not touch the Dütsch settling record.
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- Driver reads force and the small diagnostics per step only; field reads
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only at a few predeclared snapshots. Cost from Astra's no-dump timing on
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this grid.
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## Queued, not in this stage
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Leontini et al. JFS 22 (2006) Re = 200, m* = 10, zeta = 0.01, U* = 5.0 (needs
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the owners' c_crit convention and a Fig. 1 digitization). D80, literature
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claims, pinball, AMR, BC redesign, threshold changes.
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