Engineering task and calculation objective
The ZDP module calculates the pressure drop of gas-liquid two-phase flow in pipes — for horizontal and vertical upward flow as well as for vertical downward flow. It is based on the methods from Mayinger's standard work "Strömung und Wärmeübergang in Gas-Flüssigkeits-Gemischen" (Flow and Heat Transfer in Gas-Liquid Mixtures) and on the Friedel frictional pressure drop correlation, which is used in its adapted form (Chem.-Ing.-Technik 1984) for downward gas/vapor/liquid flow.
Having to calculate two-phase pressure drop is everyday business in plant engineering: in evaporator and condensate lines, riser pipes of natural circulation evaporators, blowdown and flash lines, or natural gas gathering lines with condensate formation. The pressure drop of a two-phase flow is often several times that of a single-phase flow of the same mass flux, because the phases accelerate each other and additional friction arises at the phase interface.
The module assembles the pressure drop from its components — friction, static head, and acceleration — taking the flow pattern and the void fraction into account. The result is the total two-phase pressure drop of the line as the basis for pump and compressor sizing, circulation calculations, and the hydraulic re-rating of existing systems.
Standard and calculation basis: Franz Mayinger, Strömung und Wärmeübergang in Gas-Flüssigkeits-Gemischen, Springer-Verlag 1982 Lutz Friedel, Chem. Ing. Technik 56 (1984): Reibungsdruckabfall-Beziehung für senkrecht abwärtsgerichtete Gas / Dampf / Flüssigkeits-Strömung
Calculation workflow
- Record fluid properties and mass flows: For the gas and liquid phases, the densities, viscosities, and mass flows or the flow quality are specified, along with the pipe diameter, length, and orientation of the line (horizontal, vertical upward, or downward).
- Determine flow pattern and phase distribution: Using the flow pattern maps, the flow regime (bubble, slug, stratified, annular, or spray flow) is classified and the void fraction is calculated with a slip model — in general, the phases do not flow at the same velocity.
- Calculate the frictional pressure drop: The friction component is determined via the two-phase multiplier after Friedel: starting from the pressure drop of the flow treated as single-phase, the two-phase frictional pressure drop is calculated with a correlation formed from the Froude and Weber numbers and the density and viscosity ratios. For vertical downward flow, the specifically adapted Friedel relation of 1984 is used.
- Superimpose the static head and acceleration components: From the void fraction follows the mean mixture density and thus the static head component, which acts as a loss for upward flow and as a gain for downward flow; changes in quality or cross-section yield the acceleration component.
- Report the total pressure drop: The sum of the friction, elevation, and acceleration components gives the two-phase pressure drop of the line, which is balanced against the available pressure difference or the pump head.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Density Diameter | Rhol d | – |
| Density Diameter | Rhol d | – |
| Density Gas fraction | Rhog xg | – |
| Dyn. Viscosity Tube length | Etal l | – |
| Dyn. Viscosity or | Etag | – |
| Mass flow total | Gas M | – |
| Dyn. Viscosity Tube length | Etal l | – |
| Density Gas fraction | Rhog xg | – |
| Total volume flow | V | – |
| Gas fraction | yg | – |
| Surface tension | σ | – |
| Pressure loss two phase | δp = | – |
| Variable 26 | – | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Reynolds fluid | Rel = | – |
| Reynolds gas | Reg = | – |
| Mass flux | m = | – |
| Friction factor fluid | ksil = | – |
| Friction factor gas | ksig = | – |
| Froude fluid | Frl = | – |
| Weber fluid | Wel = | – |
| Coefficient | A = | – |
| Pressure loss single phase | δp = | – |
| Two phasen multiplicator | R = | – |
Calculation options
Variable 26
Vertical upwards or horizontal flow · Vertical downwards flow
Frequently asked questions
Why is the pressure drop of a two-phase flow so much larger than that of a single-phase flow?
Because of its low density, the gas claims a large part of the cross-section and accelerates the liquid; additional shear stress arises at the wavy phase interface, and the effective velocity of the liquid phase increases. The two-phase multiplier — the ratio of two-phase to single-phase frictional pressure drop — reaches values from 3 to over 100 depending on quality and pressure. A single-phase estimate using the mixture density therefore usually underestimates the real pressure drop considerably.
What is the Friedel correlation and where are its limits?
The Friedel correlation is an empirical relation for the two-phase multiplier fitted to more than 25,000 data points and is considered one of the most accurate general correlations for pipe flow. It was developed for horizontal and upward flow; for downward flow, Friedel published a dedicated adaptation in 1984, which the module uses. Like all empirical correlations, it scatters in individual cases — deviations of ±30% must be allowed for, particularly near the flow pattern transitions.
What is the difference between flow quality and void fraction?
The flow quality x is the mass fraction of the gas in the total mass flow; the void fraction ε is the fraction of the pipe cross-section occupied by the gas. Because of the low gas density and the slip between the phases, ε is very large even at small x — at x = 0.05, the gas can already occupy more than half the cross-section. For the static head component and the mixture density, ε is decisive, not x.
Why must downward flow be treated separately?
In downward flow, gravity acts in the flow direction: the liquid runs ahead of the gas, different flow patterns and a different slip develop than in upward flow, and at low velocities the liquid can drain almost pressure-free as a falling film. The correlations developed for upward flow fail here; that is why the module uses the specifically adapted Friedel relation for this case.