Engineering task and calculation objective
The LAMO module calculates heat transfer and pressure drop in forced-circulation evaporator tubes based on the La Mont principle. In this boiler type, a circulation pump drives the subcooled water through the heated tubes; the module divides the tube run into a subcooled heating zone and an evaporation zone and determines heat transfer coefficients, overall heat transfer, required tube length and heating surface for both sections.
Anyone who wants to calculate heat transfer in flow boiling must capture not only single-phase convection (Reynolds and Nusselt numbers of the subcooled zone) but also the two-phase region: for this the module determines the characteristic numbers of the liquid and vapour fractions (Reynolds, Froude and Weber numbers), the bubble departure diameter, the maximum heat flux and the vapour quality at the outlet, including the limiting vapour quality at the stability threshold.
A key design element of the La Mont system is the perforated disk (restriction orifice) at the tube inlet: its resistance coefficient stabilises the flow distribution across parallel tubes and prevents circulation instabilities. The module calculates the required additional resistance coefficient as well as the bore diameter, thickness and pressure drop of the perforated disk – relevant for the design of forced-circulation evaporators in steam generators and waste-heat boilers.
Calculation workflow
- Divide the tube run into zones: Based on the heat inputs for the subcooled zone and the evaporation zone, the tube run is split into a single-phase and a two-phase section; the actually transferred heat duty is balanced.
- Determine single-phase heat transfer: For the subcooled zone, the Reynolds number, Nusselt number and friction factor are calculated; from these follow the heat transfer coefficient, the overall heat transfer and – together with the outer thermal resistance including the tube wall – the required tube length and area of the heating zone.
- Calculate two-phase heat transfer: In the evaporation zone, the mean heat transfer coefficient is composed of several terms (Term1 to Term4 of the Alpha2 calculation); characteristic numbers such as the Reynolds numbers of the liquid and vapour fractions, the Froude and Weber numbers, the bubble departure diameter and the maximum heat flux limit the permissible operating range.
- Sum up the pressure drops: The total pressure drop is made up of the frictional pressure drop of the subcooled zone, the two-phase pressure drop of the evaporation zone, the static pressure drop and the pressure drop of the perforated disk.
- Check stability and size the perforated disk: The vapour quality at the outlet is compared with the limiting vapour quality at the stability threshold. From the required additional resistance coefficient, the bore diameter and thickness of the perforated disk are set so that the flow distribution across parallel tubes remains stable.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Fouling resistance outside | Rf | m²·K/W |
| Heat capacity medium outside | cpa | J/(kg·K) |
| Mass flow outside | ma | kg/s |
| Heat transfer (outside) | αA | W/(m²·K) |
| Inside diameter tube | di | m |
| Outside diameter tube | da | m |
| Total tube length | l | m |
| Thermal conductivity tube | λR | W/(m·K) |
| Inlet temperature outside | Ta1 | °C |
| Outlet temperature outside | Ta2 | °C |
| Inlet temperature inside | Ti1 | °C |
| Boiling temperature medium inside | Ts | °C |
| Boiling pressure medium inside | Ps | Pa |
| Total mass flow inside | mi | kg/s |
| Added heat (total) | Qzu | W |
| Thermal conductivity water | λW | W/(m·K) |
| Density water | ρW | kg/m³ |
| Surface tension | σ1000 | mN/m |
| Surface tension | σ | N/m |
| Heat capacity water | cpW | J/(kg·K) |
| Enthalpy water | hW | J/kg |
| Dynamic viscosity water | ηW | mPa·s |
| Prandtl number (subcooled) | PrW1 | – |
| Thermal conductivity | λD | W/(m·K) |
Frequently asked questions
What is the purpose of the perforated disk at the inlet of the evaporator tubes?
In heated tubes connected in parallel, the flow can distribute unevenly: a tube with higher vapour quality has more pressure drop, receives less flow and evaporates even more strongly – a static instability (Ledinegg instability). A restriction orifice at the inlet increases the single-phase share of the pressure drop and makes the characteristic curve of each tube monotonically rising, so that the mass flow distributes itself stably.
What does the limiting vapour quality at the stability threshold mean?
Above a certain vapour quality, the circulation becomes unstable or the boiling crisis threatens (dryout of the wall film with a drastic collapse of the heat transfer). The calculated outlet vapour quality must therefore stay below the limiting vapour quality; otherwise the circulation rate, heating or tube geometry must be adjusted.
Why is the maximum heat flux reported?
The critical heat flux marks the transition from nucleate boiling to film boiling. If it is exceeded locally, the wall temperature rises abruptly, which leads to overheating damage in boiler tubes. The design must stay well below this value.
How does La Mont forced circulation differ from natural circulation?
In natural circulation, the density difference between downcomers and risers alone drives the circulation; in a La Mont boiler, a circulation pump takes over this task. This allows smaller tube diameters, free tube routing and higher mass flux, but requires the deliberate throttling of the individual tubes via perforated disks, which this module sizes.