Fluid-front transport: a conservation-speed cryogenic-front / liquid-availability state gating the TT-WF dry side

A scalar tracer per internal fluid node is advected at conservation speed by the accepted flow. This tracer gates the dry-side film/SP heat release of ttWf convection conductors. The model exposes no tunable parameter: the front moves at the mass-conservation speed of the accepted flow, full stop.

Relevant code includes src/core/fluidFront.ts (pure transport kernel + gate), solver.ts (updateFluidFrontStates (the accepted-step commit), correlations.ts (the TT-WF dry-side gate consult), schema.ts, and diagnostics.ts. Tests are located in src/core/__tests__/fluidFrontTransport.test.ts. Verification evidence is discussed in §6 below.

---

1. State and semantics

a_i ∈ [0,1]   : cryogenic front fraction of internal fluid node i

This metric measures the fraction of node i's fluid inventory that is advected cryogenic-inlet fluid: fluid that entered the network through a boundary node flagged with fluidFrontInlet: 1 since t = 0. Boundary nodes carry no state. Their configured value (default 0) is used only as the upwind value of flow entering the domain.

The following are deliberate non-identities:

quantity	why a is not it
equilibrium quality x_e(h) / liquid availability χ_l(h)	functions of the local enthalpy, not of where the fluid came from; the cold-vapor tail is the advected enthalpy field
TT-WF fWet / rewet latch	wall-side markers driven by wall cooling, not by fluid arrival (and bootstrap-degenerate: the wall must cool before the latch can set)
vapor temperature T_v	a reconstructed phase temperature, not an inventory

a carries exactly one piece of information: displaced cryogenic inlet fluid has arrived here, advanced by the accepted mass fluxes alone. A warm-filled line initializes a = 0 (there is no initial-condition knob, the model's purpose is the fill transient; a pre-chilled line is out of scope).

Opt-in surface (fully backward compatible)

• conductor.type.correlation.fluidFront: true on a ttWf convection conductor (rejected by validate.ts on any other model) does two things: enables the network-wide transport state (one a_i per internal fluid node) and gates that conductor's dry side. The gate is per-conductor; the transport state exists once any ttWf conductor opts in.
• node.fluidFrontInlet ∈ [0,1] on a boundary node marks a cryogenic inlet (1), the tracer source.
• TransientResult.fluidFront?: Record<nodeId, { fraction: number[] }>: accepted-step histories aligned 1:1 with times. Absent unless enabled.

With the flag absent everywhere, no state is allocated, no gate is consulted, and results are identical to a configuration without the flag (pinned by the existing ttWf/D-H/golden suites).

2. Transport equation and discretization

Per internal node i with (mixture) fluid mass m_i = ρ_i·V_i, the transport equation is:

d(m_i a_i)/dt = Σ_in mdot·a_up − Σ_out mdot·a_i

This is discretized with donor-cell upwinding + backward Euler on the accepted end-of-step state, the same structural choice as the solver's enthalpy transport (upwind h_sum in the energy residual) and species transport:

(m_i^{n+1} a_i^{n+1} − m_i^n a_i^n)/dt
  = Σ_j∈in(i)  |mdot_j^{n+1}| · a_{up(j)}^{n+1}
  − Σ_j∈out(i) |mdot_j^{n+1}| · a_i^{n+1}

The coupled system is linear in a^{n+1} with an M-matrix.

A_ii = m_i^{n+1}/dt + Σ_out(i) |mdot|        (> 0 if storage or outflow)
A_ij = −(inflow rate from internal neighbor j)
b_i  = (m_i^n/dt)·a_i^n + Σ_boundary inflows |mdot|·a_bnd

This system is solved directly (dense Gaussian elimination with partial pivoting: one unknown per internal node). A node with no storage and no through-flow (isolated) keeps its accepted value by a degenerate-row guard.

No transport-speed parameter exists. The front moves at the mass conservation speed of the accepted flow. The only numerical smoothing is the donor-cell/backward-Euler truncation itself: first-order Godunov-type smearing of order one cell per step (a fixed, documented discretization choice, not an exposed calibration knob (there is nothing to tune: the scheme has no ε)).

Flow reversal needs no special case: the upwind donor follows the sign of each branch's accepted mdot, so a reversed branch advects the opposite endpoint's a (kernel- and network-tested, including tracer drain-back through the original inlet).

Zero-storage nodes (V = 0) degenerate exactly to the algebraic well-mixed pass-through Σ_in mdot·a_up = Σ_out mdot·a_i (the same convention as the species-transport mixing at a junction).

3. Conservation and boundedness (proofs)

3.1 Global tracer conservation

Summing the nodal BE equations over all internal nodes, every internal branch flux |mdot|·a appears once positively (inflow to the downstream node) and once negatively (outflow from the upstream node) and cancels EXACTLY. What remains is the boundary balance:

Σ_i [(m_i a_i)^{n+1} − (m_i a_i)^n] = dt · (Σ_bnd in |mdot|·a_bnd − Σ_bnd out |mdot|·a_i)

The total tracer inventory changes only through boundary fluxes, with right-rectangle (end-of-step) quadrature: the BE-consistent convention. The identity is algebraic in the linear solve. It holds to roundoff regardless of whether the step satisfied its own mass balance. Flow reversal is covered because the boundary terms use the upwind convention in both directions.

3.2 Boundedness without clipping

Let 0 ≤ a^n ≤ 1 and 0 ≤ a_bnd ≤ 1, and assume the accepted step's converged nodal mass balance S_in,total(i) − S_out,total(i) = (m_i^{n+1} − m_i^n)/dt (the solver's own mass residual at a converged step).

• Lower bound. A has positive diagonal, non-positive off-diagonals, and is column diagonally dominant: for column j, A_jj − Σ_{i≠j}|A_ij| = m_j/dt + (outflow from j to BOUNDARY nodes) ≥ 0. Hence A is an M-matrix, A⁻¹ ≥ 0, and b ≥ 0 gives a^{n+1} ≥ 0. (No mass-balance assumption needed for the lower bound.)
• Upper bound. If any a_i^{n+1} exceeded M = max(max a^n, max a_bnd), then for the maximizing row: (m_i^{n+1}/dt + S_out,total)·a_i ≤ (m_i^n/dt)·a_i^n + S_in,total·M and the mass balance gives m_i^{n+1}/dt + S_out,total ≥ m_i^n/dt + S_in,total, forcing a_i ≤ M. Inductively a^{n+1} ≤ 1.

The scheme is bounded in [0,1] by construction at converged accepted steps (no limiter, no clipping). The implementation still post-guards: excursions within roundoff (≤ 1e-12) are clamped silently. Any larger (non-conservative) correction is clamped and counted (diagnostics.fluidFront.boundsClampCount); it can only occur if the committed step's mass balance was not actually converged. The counter therefore doubles as a commit-time convergence audit.

3.3 Adaptive step-doubling consistency

The adaptive integrator's accepted trajectory is the pair of half steps (t → t+dt/2 → t+dt), each satisfying its own converged mass balance; a single full-dt front commit would see the half-step truncation mismatch as a spurious tracer source. The commit therefore follows the accepted trajectory: updateFluidFrontStates receives the accepted half-step state and performs two half-step commits, each mass-consistent. This is the tracer analogue of the Richardson/step-doubling acceptance structure, not an extra knob.

4. The heat-exchange gate (TT-WF dry side)

For a ttWf conductor with fluidFront: true, the area-average flux becomes:

q_bar' = (1 − fWet)·g(a)·q_Dry + fWet·q_Wet,    g(a) = a²(3 − 2a)

with a being the accepted, frozen front fraction of the conductor's fluid node. g is the C1 smoothstep on [0,1]: g(0) = 0, g(1) = 1, zero slope at both ends. The bounds are fixed at [0,1] by definition: there is no fitted threshold.

Semantics of the limits:

• a = 0 (no cryogenic inventory has reached the node): no dry-side film/SP wall exchange; the h-map returns exactly h = 0, bypassing the fallback-h floor (a closed gate means zero, not ~5 W/m²K of floor leakage). A partially open gate (0 < g < 1) likewise skips the floor (the floor guards correlation failures; a gate-suppressed h below the floor is the closure working as designed) but keeps the shared under-relaxation across outer iterations.
• a = 1 (the node's fluid is cryogenic-inlet fluid): the full, untouched D-H/TT-WF dry-side map.
• fWet = 1 (wall fully rewetted): the gate is inert for any a (only the dry term is gated).

What the gate is: a closure for the unresolved relation between the cold-vapor/front state and wall exchange. The motivation: an advected cold-vapor tail can thermalize the wall well before the liquid front arrives, while in chilldown experiments the wall stays warm until the front arrives, as the real gas column ahead of the front does not exchange heat with the wall at the film/SP rate. The gate encodes exactly that, keyed on conservation-speed displacement arrival. Dry-side exchange is the only pre-front cooling path, and it is re-timed by a transport signal rather than removed.

What it is not: it does not touch the wet side (DB/NB/TB), the node's enthalpy or quality, the TT-WF front-evolution machinery (r_E keeps using the local flux map's q_Wet − q_Dry capability difference (a property of the map, not of the transport-gated exchange)), or the fluid energy budget structure. Energy conservation is untouched: gating q changes what energy is exchanged (the same gated q̄' leaves the wall and enters the mixture through the shared conductor path), and the front state carries the arrival information.

h_eff rescaling: q and h_eff share the reference (T_w − T_node), so the gated secant is h_eff·(q̄'/q̄) with no re-evaluation of the guarded secant is needed, and the TT-WF h_eff contract (finite as T_w → T_node) is preserved.

Scope: the gate currently applies to the TT-WF dry side only.

5. Solver lifecycle (accepted-step discipline)

The solver lifecycle is identical in structure to the TT-WF fWet/latch lifecycle:

• The state lives in SolverContext.fluidFront (allocated only when enabled), not in StepState. Newton/outer iterations, adaptive trial half-steps, and rejected steps only read the frozen accepted a (through the gate). Their proposals die with the discarded evaluations.
• updateFluidFrontStates(ctx, state, dt?) is the sole mutator, called by transient.ts immediately after updateConductorLatches:
  • dt omitted ⇒ t = 0 initialization: a_i = 0, previous node masses seeded from the IC;
  • dt = accepted step size ⇒ the conservative commit of §2 (two half-step commits on the adaptive path), then the snapshot is appended to TransientResult.fluidFront.
• Aborted runs return partial results sliced consistently (histories always align 1:1 with times).

Because the state is not in StepState, adaptive trial cloning needs nothing new: rejected trials never reach the commit call. The commitCount diagnostic equals the number of accepted steps (one commit per accepted step, never more).

6. Verification summary

Tests are located in src/core/__tests__/fluidFrontTransport.test.ts. Headline evidence includes:

contract	evidence
exact front travel	kernel reproduces the BE well-mixed analytical recurrence to ≤ 1e-14 per step on a 5-node line; arrival order/timings as predicted by the recurrence
global conservation	recorded-series audit on a gated 3-node LH2 chilldown: |ΔΣ(m·a) − ∫influx dt| = 6.2e-15 kg (rel ~5e-14); reversal run closes identically
bounds	every recorded a ∈ [0,1]; boundsClampCount = 0 on every run (incl. 18-rejection adaptive); randomized compressible-step sweep: 300 steps, 0 corrections
accepted-step immutability	fixed-step histories replay to ≤ 1e-9 from the kernel + recorded accepted inputs; adaptive: commitCount == stats.steps, 1:1 alignment; direct solveStateStep test: Newton + h-map never mutate a
heat-gate limits	a=0 ⇒ h = 0 exactly; a=1 ⇒ identical to ungated TT-WF; C1 monotone sweep, no jumps (`
front/wetting distinction	a half-crossing precedes latch set and fWet > 0 on every node; the kernel reads no enthalpy/quality/fWet input
backward compatibility	no fluidFront field without the flag; full pre-existing suite green