Engineering task and calculation objective
The L2.2 module calculates the pressure drop of gas-liquid flows in pipes, piping components and valves according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for heat transfer and two-phase flow. As soon as two phases flow together in a line — steam and condensate, gas and liquid, boiling refrigerant — the friction pressure drop lies well above that of a pure liquid flow at the same mass flux, because the phase interface generates additional losses and the gas phase increases the effective velocity.
Being able to calculate the two-phase pressure drop is decisive for evaporator and condensate lines, natural-circulation systems, riser lines, blowdown and flash lines, and in refrigeration engineering. In addition to straight pipe runs, the module also covers piping components and valves such as pipe bends and turns, for which dedicated two-phase approaches exist, since the phase redistribution in the bend changes the loss compared with simply transferring single-phase resistance coefficients.
The calculation follows the established correlation methods of the VDI Heat Atlas: the friction share is scaled up from the single-phase pressure drop via two-phase multipliers, with vapor quality, density and viscosity ratios of the phases and mass flux entering. Via the selected component type, the module adapts the approach to the respective piping element.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Select the component type: First, the piping element is defined: straight pipe, pipe bend or turn, or valve. The selection determines which two-phase approach and which additional geometric quantities (e.g. bend radius) are used.
- Enter the operating data and fluid properties: Required are the mass flow rates or the flow quality, density and viscosity of both phases and, where applicable, the surface tension. These quantities determine the Reynolds numbers of the phases and the ratio of the single-phase pressure gradients.
- Calculate the single-phase reference pressure drops: For the liquid and the gas phase, the pressure gradients are calculated that would result if the respective phase flowed alone (with its own share or with the total mass flow rate) through the element — the reference quantities of the multiplier methods.
- Evaluate the two-phase multiplier: From the ratio of the reference pressure gradients and the mass flux, the two-phase multiplier is determined according to the correlations of the VDI Heat Atlas; it describes by what factor the two-phase friction pressure drop exceeds the single-phase reference value. For bends and valves, the component-specific resistance coefficient is additionally corrected for two-phase flow.
- Assemble the total pressure drop: The friction share is summed with the static-head share (via the void fraction and the mixture density) and, where applicable, the acceleration share to give the total pressure drop of the line section. For piping runs, the contributions of the individual elements are added up.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Inside diameter of the tube | di | m |
| Cross section area | A | m² |
| Tube length | L | m |
| Tube angle of gradient (-90..90) | β | ° |
| Tube height difference | dH | m |
| Tube elbow radius of curvature | rRBogen | m |
| Tube elbow angle | αBogen | ° |
| Tube roughness | k | m |
| Total mass flow | Mges | kg/s |
| Mass flow of gas and steam | MGas | kg/s |
| Mass flow of liquid | MFl | kg/s |
| Mass flux | M | kg/(m²·s) |
| Mass flow of gas at the tube end | MGasa | kg/s |
| Mass flow of liquid at the tube end | MFla | kg/s |
| Vapour fraction | x | - |
| Density of the gas | ρGas | kg/m³ |
| Density of the liquid | ρFl | kg/m³ |
| Density of the mixture | ρGem | kg/m³ |
| Dynamic viscosity of the gas | ηGas | mPa·s |
| Dynamic viscosity of the liquid | ηFl | mPa·s |
| Surface tension | σ | N/m |
| Inlet pressure | P0 | Pa |
| Inlet temperature | T0 | K |
| Boiling? | 1=Siedezustand | – |
Calculation options
Boiling?
No · Yes
Auswahl Bauform
Tubes (according to Chisholm) · Tubes (according to Friedel) · Tube elbow
Frequently asked questions
Why can't I simply calculate two-phase pressure drops single-phase with the mixture density?
The homogeneous approach with mixture density and mixture viscosity underestimates the friction pressure drop over wide ranges, because it ignores the losses at the moving phase interface and the slip between the phases. In reality, the two-phase friction pressure drop is often several times the homogeneously calculated value — which is why the methods of the VDI Heat Atlas work with empirically validated two-phase multipliers.
At which vapor quality is the pressure drop greatest?
The two-phase friction pressure drop passes through a maximum over the vapor quality, typically at high qualities (often in the range of about 0.7 to 0.9): with rising quality, the flow velocity first grows; toward ẋ = 1 the loss falls back to the value of the pure gas flow. For the design of an evaporator line, the most unfavorable operating point must therefore be sought, not just the inlet and outlet states.
Why do pipe bends in two-phase flow need their own approaches?
In the bend, centrifugal force separates the phases: the liquid migrates outward, the gas inward, and downstream the flow must re-establish itself. This demixing and remixing process generates additional losses that would only be captured incompletely with the single-phase resistance coefficient and a simple multiplier. The approaches therefore consider bend geometry and flow parameters together.
How reliable are the calculated two-phase pressure drops?
Even the best correlations are fitted to measured data and show typical scatter of a few tens of percent — considerably more than single-phase calculations. The uncertainty rises near the flow-pattern boundaries and outside the data range of the correlation. For safety-relevant designs (e.g. blowdown lines), margins and limiting-case analyses should therefore be used.