Multiphase Flow Analyzer

What this tool does

Single-phase pipe calculators assume the fluid stays the same from inlet to outlet. Two-phase flow doesn't cooperate: as pressure drops along the pipe, gas expands, more liquid may flash to vapor, the flow pattern shifts, and the pressure gradient itself changes. This analyzer divides the duct into hundreds of short segments and solves them in sequence — each segment's outlet becomes the next one's inlet — so the answer reflects how the flow actually develops. Heating and cooling walls are part of the march: boiling dries the flow out, condensation wets it, and the heat-transfer coefficient follows.

Start from a preset worked example to see a complete run, then swap in your own duct, fluid, and flow rate. The charts show every quantity along the length; hover to read values off any curve.

The equations

The pressure gradient in a pipe carrying gas and liquid together is three separate effects added up, and in most real lines a different one dominates than you would guess:

-dP/dz = (dP/dz)_friction + (dP/dz)_gravity + (dP/dz)_acceleration

friction     = phi_LO^2 · f_LO · G^2 / (2 · rho_L · D)
gravity      = [alpha·rho_G + (1 - alpha)·rho_L] · g · sin(theta)
acceleration = d/dz [ G^2 · ( x^2/(alpha·rho_G) + (1-x)^2/((1-alpha)·rho_L) ) ]

Friction is larger than either phase alone would produce, because the gas drags the liquid film and roughens the interface; the two-phase multiplier phi_LO^2 is what the friction correlations actually predict. Gravity depends on how much liquid is in the pipe, not how much is flowing through it — which is why void fraction gets its own family of models. Acceleration matters because the gas expands as pressure falls.

Void fraction is the one to get right on any line that is not horizontal. Liquid moves slower than gas, so it piles up: a pipe flowing five percent liquid by mass can be forty percent liquid by volume. The default drift-flux form responds to both mass flux and surface tension:

alpha = (x/rho_G) / ( C_0 · [ x/rho_G + (1-x)/rho_L ] + u_gj/G )

C_0  = 1 + 0.12 · (1 - x)
u_gj = 1.18 · (1 - x) · [ g · sigma · (rho_L - rho_G) ]^0.25 / sqrt(rho_L)

With a heated or cooled wall, an energy balance rides along with the pressure march. Enthalpy is the quantity that is conserved, so it is the one carried between stations; quality is recovered from it at the local pressure, which is what lets the tool capture flashing:

h(z + dz) = h(z) + q · P_heated · dz / mdot
x(z)      = [ h(z) - h_f(P) ] / h_fg(P)

The selectable correlations are the standards of the two-phase literature, listed under Sources below: Friedel, Müller-Steinhagen & Heck, Lockhart–Martinelli/Chisholm and a homogeneous model for friction; Rouhani–Axelsson, Zivi, Chisholm, Butterworth's Lockhart–Martinelli fit and homogeneous for void fraction; Gungor–Winterton, Chen and Kandlikar for flow boiling; Shah and Dobson–Chato for condensation; Gnielinski, Dittus–Boelter and Sieder–Tate for single-phase convection. Flow patterns come from the Taitel–Dukler map for horizontal lines and Taitel–Barnea–Dukler for vertical ones. When your conditions leave a correlation's validated range, the run says so in its warnings rather than extrapolating silently.

Worked example: a 3 m steam evaporator

This is the Steam evaporator preset, and every number below is reproducible by hand. A 10 mm bore tube, 3 m long and horizontal, carries saturated water at 500 kPa entering at 10 percent quality, with a mass flux of 300 kg/m²s and 20 kW/m² applied at the wall. Friction is Friedel, void fraction Rouhani–Axelsson, boiling Gungor–Winterton.

Start with the flow itself:

A    = pi · D^2 / 4 = pi · (0.01)^2 / 4 = 7.854e-5 m^2
mdot = G · A        = 300 · 7.854e-5    = 0.023562 kg/s
Q    = q · pi · D · L = 20000 · pi · 0.01 · 3 = 1884.96 W
dh   = Q / mdot     = 1884.96 / 0.023562 = 80.000 kJ/kg

Now the part a single-shot calculation gets wrong. At 500 kPa water boils at 152.09 °C with h_f = 641.55 kJ/kg and h_fg = 2106.65 kJ/kg, so the inlet enthalpy is 641.55 + 0.1 × 2106.65 = 852.21 kJ/kg, and the outlet is 80 kJ/kg higher at 932.21 kJ/kg. But the pipe has lost 23.2 kPa by then, so the outlet is saturated at 476.8 kPa — 150.32 °C, h_f = 633.89, h_fg = 2112.16 — and the quality is recovered against those numbers:

x_out = (932.21 - 633.89) / 2112.16 = 0.1412

with properties frozen at the inlet pressure you would get
x_out = 0.1 + 80.0 / 2106.65 = 0.1380

The difference is flashing: falling pressure lowers the saturation temperature, and the liquid gives up sensible heat to make a little more vapour. It is worth 0.0033 of quality here — small, but it feeds straight back into void fraction, velocity and the friction gradient, and on a longer or lower-pressure line it stops being small.

The pressure drop splits into 22 789 Pa of friction, nothing at all from gravity because the line is horizontal, and 414 Pa of acceleration as the vapour expands — 23.2 kPa in total, or 7 734 Pa per metre. Average liquid holdup is 0.124, the flow is annular over the whole length, and the fluid clears the tube in 0.22 seconds.

Then the honest part. Change nothing but the friction correlation and the same 3 m of pipe gives:

Lowest to highest, that is an eighty percent spread on identical inputs, and none of the four is wrong — they are empirical fits to different data sets. That spread is the real uncertainty on a two-phase pressure drop, and it is why every run reports all four rather than quoting one as the answer. This case also trips the erosional velocity warning: 16.4 m/s against an API RP 14E limit near 11.0 m/s.

Assumptions & tips

• The march is one-dimensional and steady. Each station is a cross-section average, solved with a predictor–corrector step that closes the acceleration term against the exit state it depends on. Transients, surging and slug tracking are outside it.
• Void fraction drives the gravity term, so on vertical and inclined lines the void model matters more than the friction model. Rouhani–Axelsson is the sensible default for boiling and condensing flow; Zivi tends to underpredict at low flux, and the homogeneous model overpredicts void almost everywhere except finely dispersed or high-pressure flow.
• Between 20° and 70° neither flow-pattern map is strictly valid. The horizontal map carries an inclination term and is the one used, but treat regime boundaries in that band as approximate — and the maps were derived for round pipes, so non-circular ducts are mapped onto an equal-area circle.
• Properties come from interpolated saturation tables, not a full equation of state. Run off the end of a table and the results are flagged as extrapolated; near the critical point, treat them as indicative.
• Compare models before you trust a number. If the spread across the four friction correlations is tight, the answer is robust. If it is wide, that is genuine uncertainty and the design needs margin, a different geometry, or test data.
• Everything runs in your browser. The Word and PDF exports — inputs, results, charts, the method section with its citations, and the warnings — are generated locally and make a complete record of a run for a design file. Nothing you enter is sent anywhere.

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