Engineering task and calculation objective
This module determines the flow pattern in flow boiling in evaporator tubes per Chapter H3.2 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). In an evaporator tube with through-flow, the phase distribution changes as the vapor quality grows: from bubble flow through plug and slug flow to annular flow with a liquid film on the wall, and finally to mist/droplet flow. In horizontal and inclined tubes, gravity additionally produces stratified and wavy flow.
The flow pattern is not an academic classification but a prerequisite for any reliable evaporator design: the heat transfer coefficient, the pressure drop, and the risk of partial dryout of the upper tube surface depend directly on whether the wall is wetted. The downstream calculations for convective boiling and nucleate boiling in horizontal tubes presuppose the flow pattern determined here.
Input quantities are mass flux, vapor quality, hydraulic diameter, and inclination angle of the tube, together with the density and viscosity of both phases and the surface tension; the result is the position of the operating point in the flow pattern map.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Capture the geometry and operating data: The hydraulic diameter (for a circular tube, the inside diameter), the inclination angle of the tube, the mass flux, and the vapor quality define the operating point.
- Provide the property data of both phases: Density and dynamic viscosity of liquid and vapor as well as the surface tension are evaluated at the boiling pressure; they determine the balance of forces between inertia, gravity, and capillarity.
- Evaluate the transition criteria of the flow pattern map: The boundary curves between stratified, wavy, plug/slug, annular, and mist flow are calculated as functions of mass flux and vapor quality; the inclination angle shifts the gravity-controlled boundaries.
- Assign the flow pattern: The operating point is compared with the boundary curves and assigned to the applicable flow pattern. Since the vapor quality changes along the evaporator tube, the evaluation should sensibly be repeated for several tube positions.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Hydraulic diameter (tube = di) | d | m |
| Vapour mass fraction | ẋ | -- |
| Mass flux | ṁ | kg/(m²·s) |
| Surface tension | σ | mN/m |
| Density | ρL | kg/m³ |
| Density | ρG | kg/m³ |
| Dynamic viscosity | ηL | mPa·s |
| Dynamic viscosity | ηG | mPa·s |
| Angle of inclination of the tube | Θ ( ≤10° ) | ° |
| Flow pattern | Strömungsform | - |
Frequently asked questions
Why is the flow pattern so important for evaporator design?
Because it decides whether the heated wall is wetted. In annular flow, a liquid film carries the heat transfer and α is high; in stratified flow in a horizontal tube, the upper tube surface is covered only by vapor, the local heat transfer collapses there, and the wall temperature rises. Pressure drop, pulsation tendency (slug flow), and erosion also depend on the flow pattern.
What is the difference between vapor quality and void fraction?
The vapor quality x is the mass fraction of vapor in the total mass flow, x = ṁ_vapor/ṁ_total. The void fraction, by contrast, describes the cross-sectional area fraction of the vapor phase and cannot be converted directly from x because of the slip between the phases. The flow pattern map is spanned by the vapor quality and the mass flux.
Do the maps also apply to inclined tubes?
The module accounts for the inclination angle: even a slight inclination from the horizontal changes the gravity-controlled transitions considerably — in upward flow, stratified flow disappears quickly; in downward flow, its region expands. For vertical tubes, the stratified patterns vanish entirely; there, bubble, plug/slug, annular, and mist flow dominate.