Fluid Property Lookup: Method

The Formulations, Their Ranges and the Reference States

Scope

The tool returns the thermodynamic and transport properties of one fluid at one state: water and steam, eight ideal gases and four refrigerants. It is a property look-up, not a cycle or heat-transfer calculation; the Power and Refrigeration Cycles tool and the thermal-fluids tools of this area call the same library (fluidprops_lib.php) for their states, so a number read here is the number those tools use. Every value is computed, nothing is read from a printed steam table: water from the IAPWS Industrial Formulation 1997, gases from the NASA Glenn polynomials, refrigerants by interpolation in NIST Chemistry WebBook tables. The library is checked against every verification table printed in the IAPWS releases, against the NIST-JANAF rows for the gases and against freshly fetched WebBook points for the refrigerants (test-scripts/test_fluid_properties.php).

Units and the state pair

Pressure goes through the site's unit dictionary (MPa, kPa, bar, psi …). Temperature is a plain number, °C in SI mode and °F in USCS mode, because the dictionary's absolute temperatures carry offsets the unit engine cannot apply; the unit switch does not convert it. Enthalpy, entropy and the other results without a dictionary type are printed with their unit named: kJ/kg or Btu/lb (1 Btu/lb = 2.326 kJ/kg exactly, the international-table Btu), kJ/(kg·K) or Btu/(lb·°R) (1 Btu/(lb·°R) = 4.1868 kJ/(kg·K)), m³/kg or ft³/lb, µPa·s or lb/(ft·h), W/(m·K) or Btu/(h·ft·°F). The state is fixed by one of five pairs: p-T for every fluid; p-h, p-s, p-x and T-x for water and the refrigerants (an ideal gas has no dome and its enthalpy is a function of temperature alone, so only p-T applies). With a quality pair the state sits on the saturation line and the single-phase properties c_p, c_v, w, μ and k are not defined; the lever rule gives v, u, h and s.

Water and steam: IAPWS-IF97

The Industrial Formulation 1997 (revised 2012) divides the p-T plane into five regions (its Figure 1): region 1, the compressed liquid from 273.15 K to 623.15 K between the saturation pressure and 100 MPa, a Gibbs-energy equation in p and T with 34 terms; region 2, the superheated and supercritical vapour up to 1073.15 K and 100 MPa, a Gibbs equation with an ideal-gas and a residual part (43 terms), plus a supplementary equation for the metastable vapour below 10 MPa; region 3, the near-critical fluid between 623.15 K and the B23 line up to 100 MPa, a Helmholtz-energy equation in density and temperature (40 terms) whose density at a given p and T the tool finds by scanning the isotherm and refining the physical root by bisection, taking the liquid branch above the saturation pressure and the vapour branch below it; region 4, the saturation line, an implicit quadratic solved explicitly both for p_s(T) and T_s(p) from the triple point (273.16 K, 611.657 Pa) to the critical point (647.096 K, 22.064 MPa); and region 5, the high-temperature vapour from 1073.15 K to 2273.15 K up to 50 MPa (undissociated water). All properties follow from the dimensionless energy and its derivatives: v, u, h, s, c_p, c_v and the speed of sound w. For a state given by p-h or p-s the release's backward equations T(p,h) and T(p,s) of regions 1 and 2 (three sub-regions in region 2, split at 4 MPa and at s = 5.85 kJ/(kg·K)) give the temperature directly; the tool then refines it against the basic equation so that the printed state is consistent to better than 10⁻⁶ K, and uses bisection in regions 3 and 5. Saturated liquid and vapour below 623.15 K come from regions 1 and 2 at p_s(T); above it from the two branches of region 3, which the release built to satisfy the Maxwell criterion on the saturation line. The reference state is the one all modern steam tables share: u = s = 0 for the saturated liquid at the triple point, so h = 0.000612 kJ/kg there. IF97 reproduces the scientific formulation IAPWS-95 within about 0.05 % in volume and 0.03 % in enthalpy in regions 1 and 2 and somewhat more loosely in region 3; the default case of the tool (1 MPa, 300 °C) is printed beside the WebBook's IAPWS-95 values for that comparison.

Viscosity and thermal conductivity of water

The viscosity is the IAPWS 2008 formulation (Huber et al. 2009): a dilute-gas term in temperature times a density term, μ = μ₀(T) μ₁(T, ρ), in its industrial form, that is with the critical enhancement μ₂ set to one, which matters only within a few kelvin and a few tens of kg/m³ of the critical point, with the density from IF97 as the release recommends. The thermal conductivity is the IAPWS 2011 formulation (Huber et al. 2012): k = k₀(T) k₁(T, ρ) + k₂, where the additive critical enhancement k₂ is computed in the release's industrial form from the IF97 heat capacities, the isothermal compressibility (∂ρ/∂p)_T of the IF97 region equation and the viscosity above; it is small away from the critical region but not negligible (about 2.6 % at 20 MPa and 620 K), and the tool reproduces the release's program-verification tables for regions 1, 2 and 3 term by term. Both are valid over the IF97 range; the conductivity should not be trusted above about 1500 K, where dissociation sets in.

Ideal gases: the NASA Glenn polynomials

For air, N₂, O₂, CO₂, H₂O, Ar, H₂ and CH₄ the tool evaluates the nine-coefficient polynomials of McBride, Zehe and Gordon (NASA/TP-2002-211556): c_p/R = a₁T⁻² + a₂T⁻¹ + a₃ + a₄T + a₅T² + a₆T³ + a₇T⁴ with the matching integrals for h and s and the two integration constants, in two temperature intervals (200–1000 K and 1000–6000 K). These are the data behind NASA's Chemical Equilibrium with Applications program; against the NIST-JANAF tables they agree to about 0.1 % in c_p and better in s. The enthalpy carries the NASA reference: the enthalpy of formation at 298.15 K is included (zero for the elements and for air, which the report defines as a reacting mixture of N₂, O₂, Ar and CO₂ with M = 28.965), so h of CO₂ is strongly negative; the sensible part h − h(298.15 K) is printed beside it for cycle work. The entropy is absolute, at the entered pressure, from the standard-state value at 1 bar with s − s° = −R ln(p/1 bar). The density is the ideal-gas p/(RT), the speed of sound √(γRT) with the local γ = c_p/c_v; neither is meaningful near saturation or at high reduced pressure, where a real-gas equation is needed (water vapour below about 150 °C and CO₂ near its dome are the cases to watch: use the IF97 water or the R-744 tables instead). Air also gets the Sutherland viscosity μ = 1.458 × 10⁻⁶ T^3/2/(T + 110.4) Pa·s and the conductivity formula of the U.S. Standard Atmosphere 1976 (equations 51 and 53), good to a few per cent from 200 K to about 1500 K; the other gases have no transport properties in this tool.

Refrigerants: NIST WebBook tables

R-134a, ammonia (R-717), carbon dioxide (R-744) and propane (R-290) come from the NIST Chemistry WebBook's fluid pages, which evaluate the reference equations of state of Tillner-Roth and Baehr, Tillner-Roth et al., Span and Wagner, and Lemmon, McLinden and Wagner. The library holds the saturation table at every kelvin from the triple point to the last whole kelvin below the critical temperature (liquid and vapour density, internal energy, enthalpy, entropy, c_v, c_p, speed of sound, viscosity, conductivity, surface tension) and fifteen to seventeen superheated isobars from the lowest useful pressure to about 90 % of the critical pressure, each tabulated every 5 K from just above saturation to the upper limit of the equation. A saturation state is interpolated linearly between the kelvin rows (ln p linearly); a superheated state is interpolated along the two isobars that bracket the pressure at the same superheat T − T_sat, then linearly in ln p between them (ln v for the volume). Checked against freshly fetched WebBook points midway between the stored isobars, the interpolation error is a few tenths of a per cent in v and much less in h and s (the figures per fluid are in the test and in References/Fluid-Properties/README.md). The tables stop at the critical pressure: a supercritical state (a transcritical CO₂ gas cooler) is refused with a message. A compressed-liquid state is not tabulated either; the tool returns the saturated liquid at the same temperature (or at the same enthalpy or entropy) and says so, which is the usual approximation for a subcooled liquid at moderate pressure. The reference state is the WebBook default for these fluids, the IIR convention h = 200 kJ/kg and s = 1 kJ/(kg·K) for the saturated liquid at 0 °C, so enthalpies agree with the common refrigerant tables but not with ASHRAE's older convention or with the "h = 0 at −40 °C" tables.

Reading the results

The State section names the region (water) or phase, lists every property with its unit and, for a two-phase state, the quality. The Saturation section gives p_sat at the state's temperature and T_sat at its pressure with the saturated liquid and vapour rows and the fg differences, which is what a cycle calculation usually needs next; both are omitted beyond the critical point. The two tables around the state step the pressure by a percentage at constant temperature and the temperature by a fixed step at constant pressure, so that a derivative can be read by hand and the behaviour across a region or phase boundary seen; a row that falls outside the formulation says so. The figures are the T-s diagram with the dome, ten isobars and the state (for water the state's own isobar is added in black) and the p-h diagram with ten isotherms (for a refrigerant over the vapour region only), or for a gas the c_p(T) and γ(T) curves. The charts are drawn from the same library calls as the tables.

Limits

Water: 273.15 K to 1073.15 K up to 100 MPa and 1073.15 K to 2273.15 K up to 50 MPa; ice and the sublimation line are not covered, and states between 273.15 K and 273.16 K below the melting pressure are metastable. The region-3 density search is robust for stable states; within about 0.01 kg/m³ of the critical density on the critical isotherm the transport formulations are, by their own statement, unreliable. Gases: 200 K to 6000 K for the polynomials, ideal-gas behaviour assumed throughout. Refrigerants: states on the saturation line and in the tabulated vapour region only; no supercritical, no compressed liquid beyond the saturated-liquid approximation, no mixtures or blends (R-410A, R-407C) and no surface-tension or dielectric data in the tool. No fluid other than these thirteen; engine oil, glycol-water and brines were left out because no public-domain source of their properties was found.