Engineering task and calculation objective
This module calculates film condensation of superheated vapor according to Section J1.6 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019), the standard German reference work for heat transfer. When superheated vapor meets a wall whose temperature lies below the saturation temperature corresponding to the pressure, it condenses despite its superheat: the vapor cools in a boundary layer down to the interface temperature and, in addition to the enthalpy of vaporization, releases its superheat enthalpy to the condensate film.
In practice this case arises in many plants, because steam from superheaters, turbine extractions, or downstream of pressure-reducing stations rarely arrives exactly saturated: condensers, heating coils, and start-up condensers are regularly fed with superheated steam. Anyone who wants to calculate condensation of superheated vapor must clarify how strongly the superheat actually changes the heat transfer and the condensing mass flux — usually the effect is moderate as long as the wall stays below the saturation temperature.
The module builds on the heat transfer coefficient according to Nusselt and corrects it for the contribution of the specific superheat enthalpy; in addition, the interface temperature, the mass flux at the phase interface, and the heat flux are reported.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the vapor state and wall temperature: Inputs are the pressure and temperature of the superheated vapor, the saturation temperature corresponding to the pressure, and the wall temperature; the superheat of the vapor follows from the temperature and saturation values.
- Provide the fluid properties: Required are the molar mass, the enthalpy of vaporization, and the specific heat capacity of the superheated vapor; the condensate properties are evaluated at the mean film temperature, the vapor properties at the mean vapor temperature.
- Calculate the heat transfer according to Nusselt: For the condensate film, the heat transfer coefficient is determined per Nusselt's film condensation theory using the temperature difference between saturation and wall temperature.
- Account for the superheat: The specific superheat enthalpy Δh<sub>ue</sub> = cp<sub>D</sub> · (ϑ<sub>∞</sub> − ϑ<sub>Ph</sub>) is added to the enthalpy of vaporization; via the interface temperature and, where applicable, the accommodation coefficient, the state at the phase interface is determined consistently.
- Evaluate the flux densities: The results report the mass flux of the condensing vapor at the phase interface and the heat flux at the wall — the condensed quantity per unit area is somewhat smaller than for saturated vapor at the same heat flux, because the superheat also has to be removed.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure of the superheated vapor | p∞ | Pa |
| Temperature of the superheated vapor | ϑ∞ | °C |
| Wall temperature | ϑW | °C |
| Molar mass | M | kg/kmol |
| Heat of evaporation | Δhv | J/kg |
| Heat transfer coefficient acc. to Nusselt | α | W/(m²·K) |
| Specific heat capacity of superheated vapor | cpD | J/(kg·K) |
| Accommodation coefficient | σAkk | – |
| Critical pressure | pkrit | Pa |
| Critical temperature | ϑkrit | °C |
| Acentric factor | ω | – |
| Constant | A | – |
| Constant | B | – |
| Constant | C | – |
| Constant | W1 | – |
| Constant | W2 | – |
| Constant | W3 | – |
| Constant | W4 | – |
| Condensation temperature at the pressure p∞ | ϑS,∞ | °C |
| Dampfdruckgleichung | Dampfdruckgleichung | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Vapor pressure at phase layer temperature | pPh | Pa |
| Mean film temperature | ϑF | °C |
| Mean vapor temperature | ϑD | °C |
| Spec. superheating enthalpy Δhue = cpD · (ϑ∞ - ϑPh) | Δhue | J/kg |
| Mass flux at phase layer | ṁ (52) | kg/(m²·s) |
| Heat flux | q̇ | W/m² |
| Phase layer temperature | ϑPh (53) | °C |
Calculation options
Dampfdruckgleichung
Vapor pressure equation for water · Ambrose-Walton equation · Antoine equation · Vapor pressure equation 1
Frequently asked questions
Does superheated vapor condense at all on a wall above the dew line?
The decisive quantity is the wall temperature, not the vapor temperature: if the wall lies below the saturation temperature for the prevailing pressure, a condensate film forms whose surface settles practically at the saturation temperature — the superheated vapor cools down onto it in a thin boundary layer. If, on the other hand, the wall lies above the saturation temperature, no condensation takes place, only single-phase gas cooling with markedly poorer heat transfer.
How much does the superheat improve the heat transfer?
Only slightly. At typical superheats of 20 to 100 K, the superheat enthalpy cp·Δϑ_ue is usually only a few percent of the enthalpy of vaporization; the correction to the heat transfer coefficient is correspondingly small. Practically more important is the effect on the condensate quantity: part of the transferred heat goes into removing the superheat and is not available for condensation.
Which temperature difference governs the Nusselt calculation?
The difference between the saturation temperature (or interface temperature) and the wall temperature — not the difference to the superheated vapor temperature. A common mistake is to calculate with the full difference of vapor temperature minus wall temperature; that overestimates the heat flow, because the thermal resistance of the condensate film only sees the saturation difference.
When must a molecular-kinetic correction be added?
At very low pressures or for substances with a small accommodation coefficient, the mass transfer resistance at the phase interface becomes noticeable; the interface temperature and the vapor pressure at the interface are then determined iteratively, as in metal vapor condensation. For typical steam applications at atmospheric pressure and above, this correction is negligible.