Solver changelog

Changes

• The liquid solver's water reference pressure is inferred from the boundaries (fluid node's own pressure, else the highest pressure boundary, else 1 atm) or set on the fluid node; the editor and the API no longer send a reference of their own.
• The fluid basis — temperature, absolute pressure, density, viscosity and how the pressure was chosen (set, inferred, assumed, or as entered) — is reported on every liquid run.
• A new warning names runs whose water properties were evaluated at an assumed liquid state.

Remaining approximations

• The liquid solver uses one density and one viscosity for the whole network; the inferred pressure is a convention, not necessarily representative of every pipe. Water density moves about 0.045 % per MPa, so this matters only on very high-pressure or very hot systems — where the property reference pressure field is the right tool.

Changes

• On liquid networks whose only control valves are flow control valves, the starting flow of every pipe takes its direction from a pipes-only head ordering of the network (each fitting a zero-resistance junction); magnitudes and starting heads are unchanged.

Changes

• A control valve's inlet pipe is the one attached to its inlet port, read from the drawing's port names; models saved without port names keep the previous rule.
• On lines whose only control valves are flow control valves, the iteration's starting flows take their direction from the pressure ordering of the pipe network, so a reversed-drawn pipe starts with the physical sign. Regulator lines, pumps, blowers and prescribed-flow boundaries keep their own starting points.

Changes

• Reporting only, added 11 October: every converged gas run (isothermal, adiabatic, diabatic) now carries the same acceptance diagnostics the liquid solver has reported since 7 October — the largest remaining local mass imbalance in kg/s, momentum imbalance as an equivalent pressure in Pa, energy imbalance as an equivalent temperature in K, each control-valve setpoint error, and for every held pressure regulator the distance from its setpoint against the regulator iteration's stopping tolerance (0.1 % of the setpoint, at least 1 Pa). The Reports header, the solver briefing and the PDF, CSV and XLSX exports say "Converged using relaxed tolerances" when the final state is within the relaxed figures but not the tight ones, and name the limiting equation. Converged answers, the success or failure of a run and the regulator tolerances are unchanged; the diagnostics are read off the final state after the solve.
• The regulator iteration's trial solves carry the exact derivative of the valve's pressure drop with respect to the flow, the valve-inlet pressure and the valve-inlet temperature (through the connection state), where before they held it fixed during each trial solve.
• If a trial solve fails with the exact derivative, the solver still retries it once with the previous approximate treatment before judging the trial. No previously successful case was lost in the measured 360-case sweep.

Remaining approximations

• The friction factor's dependence on flow stays frozen in the solver's derivatives (a convergence detail; converged answers are unaffected).

Changes

• The energy balance at a junction is the exact mixing rule: the mass-weighted stagnation enthalpy of the arriving streams (each less the heat its pipe lost) equals the stagnation enthalpy of every leaving stream. Kinetic energy no longer appears in the junction balance; it appears where it belongs, in each pipe end's own static state.
• A pipe end's static temperature solves h(P, T) + G²/(2ρ²) = h₀ for that end's actual pressure (after a one-sided fitting loss, or the frozen choked exit pressure) and mass flux, with the same real-gas enthalpy, ideal-gas or IAPWS-IF97 property model the rest of the solver uses; the derivatives of every momentum row through those states are analytic (implicit function theorem), including the fitting-loss and heat-exchange chains, manual-K tee losses, and the orifice's Reynolds-number dependence.
• Reported temperatures: a node's `temperature` is the static temperature of the connection whose pressure the node pressure represents (plain fittings, back-pressure valves, single-inlet junctions and sinks: the inlet; pressure-reducing valves: the outlet; flow-control valves: a consistent virtual state at the midpoint pressure; a junction where several streams meet: the mass-weighted mean of the arriving connections); pipe `temperatureIn` / `temperatureOut` are the two pipe-end states; where a node's connections differ by more than 0.05 K the node also carries `connectionTemperatures` per pipe, and the results table lists them. Node density follows the reported state; a node's volumetric flows in and out are each summed at their own connection's pressure and temperature (a methane valve 70 → 20 bar now reports 2.2 m³/s entering and 7.6 m³/s leaving the same 115 kg/s). Heat exchange along a pipe is evaluated from the pipe's own inlet pressure, so a valve's pressure drop is no longer counted a second time in the downstream pipe's heat exchange (the pipe's own pressure loss still cools a real gas by the Joule–Thomson effect).
• Validated against the ideal-gas closed form of conserved stagnation enthalpy, an independent Fanno march of each pipe of the mixed tee (exit pressures within 0.5 % of the drop, temperatures within 0.1 K), and a per-node energy audit on unrounded solver states (imbalance below one part in a million, including a heated junction, a three-leg junction, CO₂ and steam).

Remaining approximations

• A junction's reported temperature is one of its connection temperatures; a thermometer in a plenum would read close to the stagnation value, which is not exposed in this release.
• The friction factor's dependence on flow stays frozen in the solver's derivatives (a convergence detail; converged answers are unaffected).
• Lines whose resistance sits in a single valve or orifice now start the iteration from a flow the component can pass; a pressure-reducing regulator on a deep gas expansion is retried from a fresh start when a warm start fails. Both change how the solver gets to the answer, not the answer.

Changes

• The series test is topological rather than a pipe count: no internal node with three or more open pipes. A branched, pressure-driven network seeds each pipe at A·√(2ρΔP/(fL/D)) for its own area, length and diameter, the same estimate the first pipe always received.

Remaining approximations

• At a junction whose legs leave at very different speeds, the energy balance carries a single static temperature for the junction, so the slow leg inherits part of the fast leg's kinetic-energy deficit: in the measured case the sink on the slow 300 mm leg reads about 10 K cold while total energy is conserved. The error scales with the kinetic energy of the fast leg and is not confined to high speeds: with both sinks at 5.9 bar(a), every velocity below Mach 0.17, the slow sink still reads 299.0 K where conserved upstream stagnation enthalpy gives 300.0 K.

Changes

• The passive pressure-squared ordering that already seeded pipes-only networks now also signs the flow of networks with passive fittings, treating each fitting as a zero-resistance junction for the ordering only; flow magnitudes and pressure seeds are untouched, so a forward drawing's starting point is byte-identical and a reversed drawing is the exact mirror of the forward solve.
• The isothermal repair re-solves from the two-sided loss allocation and, failing that, from displaced flows, and only then reports the capacity error. It leaves alone any fitting upstream of a discharge that is choked at the isothermal limit, where pressure legitimately stops falling along the duct and the choking treatment governs; a fitting on a sibling branch of the same network is still checked.

Remaining approximations

• Very small orifices on a strongly non-ideal gas (a 20 mm bore in a 300 mm CO₂ line, β = 0.07) can still fail to converge on the isothermal solver in either drawing direction; the adiabatic solver solves them.
• The starting-point direction comes from a pipes-only pressure ordering that ignores elevation, so a gas line driven against its pressure gradient by static head alone starts with the wrong sign and relies on the solver to turn it.
• The adiabatic solver does not yet converge a tee network with one branch discharging choked (the isothermal solver does); this predates both changes.

Changes

• A fitting's loss is now computed as a magnitude from the flow through it, K·ṁ²/(2ρA²), and the solver applies it against the flow direction at the fitting's downstream pipe end; the loss used to be computed as K·ṁ|ṁ|/(2ρA²), which already carried the flow sign, so the solver's own direction handling applied it a second time.
• Measured: forward and reversed drawings of an air orifice (60 mm bore in a 300 mm line, 6 → 5 bar), a wide-open gate valve at its automatic K (6 → 5.5 bar), a 300 → 150 mm reducer, a K = 50 elbow, a methane orifice (70 → 50 bar) and a methane reducer now agree to the last reported digit in mass flow, fitting inlet and outlet pressure and outlet temperature on both gas solvers.

Remaining approximations

• A reversed-drawn fitting on a strongly non-ideal gas across a large pressure ratio (CO₂ 40 → 5 bar across a 30 mm orifice, or a methane Kv valve 70 → 20 bar) may still fail to converge; the forward drawing of the same line solves. This is a convergence limit of the reversed starting point, present before this change and the same for Kv valves, which were never affected by the sign. Redraw the pipes in the flow direction.
• Near-sonic isothermal runs can have more than one mathematical root; a reversed drawing may land on a different one from the forward drawing (one of them with a pipe Mach number above the isothermal limit). Use the adiabatic solver for such lines.

Changes

• At each Gauss point of the along-pipe density integral the temperature solves h(P, T) + G²/(2ρ²) = h₀,up − q(s), with h₀,up the upstream stagnation enthalpy, G the mass flux and q(s) the heat lost per unit mass up to that point under the same exchange profile the pipe's heat term integrates. For an ideal gas without heat exchange this is the Fanno static temperature; for a real gas it carries the Joule–Thomson cooling along the pipe.
• The integral's derivatives are exact through the implicit function theorem, including a new mass-flow term through the kinetic energy and the dependence of the heat profile on the upstream state and on the mass flow, which were previously frozen.
• Measured on a near-ideal Fanno duct (methane-like, 5 → 1.5 bar, 50 m): the along-pipe integral now reads +0.007 % against the independent integration where the previous temperature path read +1.1 %, so the earlier restriction keeping near-ideal gases on the two-point form is no longer needed for accuracy; it is kept only so those results stay byte-identical.
• Real-gas pipes take the 12-point integration rule directly instead of a 5-point rule with a refinement test, now that every point carries an energy solve.

Remaining approximations

• Pressure is still taken linear in position between the pipe ends; the residue on a heated air pipe at one segment is +0.5 % in flow, unchanged, and vanishes with refinement.
• The heat profile along a real-gas pipe takes its Joule–Thomson cooling as uniform in position; a CO₂ pipe entering at ambient and dropping 20 → 10 bar reads 0.9 K warm at the outlet as a single pipe, 0.06 K in four segments.
• The compressibility factor's dependence on the mean temperature stays frozen in the solver's derivatives (a convergence detail; converged answers are unaffected).
• Each integration point is now a small energy solve, so the along-pipe evaluation does more work per pipe; the Peng–Robinson cubic is solved analytically at the same time (identical roots to rounding), which more than pays for it — a single dense-CO₂ pipe solves in about 14 ms instead of 21 ms, a cooled one in 31 ms instead of 40 ms. Networks of many real-gas pipes with control valves run at two to three times their previous time.

Changes

• Enthalpy per unit mass is h(P, T) = h_ig(T) + h_dep(T, P)/M with the Peng–Robinson departure h_dep = RT(Z − 1) + (T·da/dT − a)/(2√2·b)·ln[(Z + (1 + √2)B)/(Z + (1 − √2)B)] from the same critical properties and Z the momentum equations already use. Valves, regulators and orifices need nothing special: their node energy balance is isenthalpic once h depends on P.
• The ideal-gas part uses a temperature-dependent Cp(T) table for methane, CO₂, ethane, propane, butane, ethylene, ammonia, hydrogen sulphide and sulphur dioxide, each checked against an independent reference (NIST Shomate or literature Cp points, within 0.4 % over 300–400 K). Natural gas (a pseudo-component) and the refrigerant presets keep the constant Cp from γ for the ideal part until a reference validates their tables.
• The energy equations' Jacobian carries the real-gas terms exactly: h(P, T) on the mass-flow columns, the real Cp(P, T) on the temperature columns and new pressure columns for ∂h/∂P, verified against central differences on forward, reversed and terminal-sink rows.
• Heat exchange along a real-gas pipe integrates the energy balance with the Joule–Thomson cooling as a distributed source: Q = ṁ·Cp·[(T_in − T_ambient)·E + ΔT_JT·(E/NTU − 1)], E = 1 − e^−NTU, ΔT_JT = μ_JT·ΔP. It is the previous form when ΔT_JT = 0 and lets a pipe entering at ambient take in the whole JT cooling at large NTU. Measured against an independent coupled march on CO₂ entering at 15 °C, 20 → 10 bar, 2 km of 100 mm pipe: outlet within 0.9 K as a single pipe, 0.06 K in four segments.
• Real-gas runs start from an isenthalpic temperature estimate and a mass-flow estimate capped at the capacity of the most restrictive valve or orifice, which the strongly non-linear energy equations need; ideal-gas runs keep their previous starting point.
• A valve, regulator or orifice whose outlet falls below 0 °C after the expansion now carries a conditional advisory stating the solved temperature and that, if free water is present, hydrate formation or freezing may be a risk — which depends on water content, pressure and composition and can occur above 0 °C.

Remaining approximations

• The Peng–Robinson departure is the model's main uncertainty: at low reduced pressure it understates methane's enthalpy departure by 12–16 %, which is the 3.5 K excess cooling in the 70 → 4 bar case above; CO₂ and ethane are within 1 % of NIST, propane 8 % (partly cancelled by its ideal part). No benchmark exists for the natural-gas pseudo-component, so its uncertainty is not characterised. Hydrogen's inversion behaviour is out of scope (hydrogen is treated as ideal).
• Along a dense real-gas pipe the density quadrature still takes the temperature linear in position between the pipe ends; with Joule–Thomson cooling the temperature follows the pressure, which falls faster toward the outlet, so a single long pipe at high density over-predicts flow — 3.1 % for CO₂ at 350 K, 150 → 80 bar through 10 km of 100 mm pipe — converging to 0.2 % in four segments. An energy-consistent temperature path is the planned follow-up.
• The distributed-source heat form takes the JT cooling as uniform along the pipe; the true cooling concentrates toward the outlet (0.9 K on the benchmark above as one pipe).
• Deep-choke Kv valves at pressure ratios above about 5:1 remain outside the adiabatic solver's convergence envelope, with or without real-gas enthalpy; an orifice at the same conditions solves.

Changes

• Heat loss or gain per pipe is Q = ṁ·Cp·(T_in − T_ambient)·(1 − e^−NTU), the integrated form of ṁ·Cp·dT/dx = −U·πD·(T − T_ambient). Outlet temperature relaxes toward ambient and cannot cross it, and for a given mass flow the outlet temperature no longer depends on how the pipe is split into segments (the mass flow itself can still show a small segment dependence — see remaining approximations). The published diabatic validation case now references this integrated balance (400.0 K, reproduced to 0.1 K).
• For fluids with Peng–Robinson critical properties on Colebrook pipes, the isothermal momentum balance evaluates 2·R·T·∫ρ dP by Gauss–Legendre quadrature (5 points, 12 where the compressibility factor varies strongly) and takes the acceleration term on the density ratio. A single mean-pressure Z is exact only while Z is near-linear across the pipe. Measured against an independent numerical integration of the same property models: 0.01 % on the CO₂ example above.
• The adiabatic and diabatic solvers walk the same integral along a temperature path — linear between the pipe ends for an adiabatic pipe, the exponential heat-exchange profile for a diabatic one — for non-ideal gases and for any pipe with heat exchange; ideal gases without heat exchange keep the previous endpoint form, so published Fanno cases are unchanged. Measured against an independent integration of the coupled momentum and energy equations: within 0.15 % for the dense CO₂ example and 0.1 % for the cooled air example above.
• The acceleration term in both gas momentum equations scales with ṁ², as the physics requires, rather than with the signed ṁ|ṁ| of wall friction. Reversing a drawn pipe now changes only the sign of its mass flow.
• Reported pressure-loss breakdowns (friction, acceleration, elevation, components) for adiabatic pipes now replay the same terms the solver used, including the sonic exit pressure of a choked pipe, so they sum to the end-to-end drop.

Remaining approximations

• The along-pipe temperature path carries no kinetic temperature drop, so for near-ideal gases at high Mach number the previous endpoint form remains in use; an energy-consistent path is planned.
• The coupled flow calculation still carries approximations beyond the heat balance: dense CO₂ with strong cooling in a single long pipe shows 0.7 % more flow when split into four segments (330 K CO₂, 90 to 60 bar, 2 km of 100 mm pipe cooled to 10 °C ambient); splitting the pipe removes it.
• Steam keeps a single IAPWS-IF97 compressibility factor per pipe, and the Weymouth and Panhandle equations keep their own standard forms.

Changes

• FCV sizing Kv from the true inlet state (IEC 60534-2-1), rated valves still report their rated value.
• Gas viscosity scales with (T/T_ref)^0.7 along adiabatic pipes for non-water gases.
• Pressure-driven seeding of fixed-flow gas networks from the boundary pressures.

Changes

• Fittings list per pipe with Crane TP-410 K = n·f_T; EPANET minor losses import as a custom fitting.
• Fixed Darcy friction factor per pipe (Darcy–Weisbach only); the calculation trace labels it as user-specified.

Changes

• One-sided pressure-drop allocation for plain drop components in the adiabatic solver, matching the isothermal solver.
• Spurious over-capacity roots are rejected by a post-solve component outlet-pressure audit and repaired by a re-solve.

Changes

• Regulators are internal nodes with a solved Kv; a setpoint that cannot be held is released to the natural state with a warning, and a rated maximum Kv is honoured as a fixed restriction.

Changes

• Flow-equation selector for gas networks; efficiency factor E per pipe; validated against Menon's worked examples to within 0.1 %.

Changes

• Average-pipe-pressure Z per edge in both compressible momentum residuals.
• Asymptotic choked-flow capacity for IEC 60534 gas valves.

Changes

• One-sided pressure-drop allocation for plain drop components in the isothermal solver.