Engineering task and calculation objective
This module calculates heat transfer in dropwise condensation according to Section J3 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019), the standard German reference work for heat transfer. If the condensate does not wet the surface completely, the vapor deposits not as a closed film but in the form of individual droplets that grow, coalesce, and roll off, continuously exposing fresh, highly effective condensation area. The heat transfer coefficients are consequently five to ten times higher than in film condensation — for steam, values well beyond 100 kW/(m²·K) are possible.
In practice, dropwise condensation is of interest wherever high power densities are deliberately targeted with hydrophobized surfaces (promoters, coatings, noble metals), for example in compact condensers or test facilities. The module calculates the heat transfer coefficient from the saturation and wall temperatures and accounts for the thermal conductivity of the tube material as well as the inert gas content of the vapor — both quantities substantially limit the achievable heat transfer.
Designing for dropwise condensation, however, requires that the wetting state be secured permanently; without a stable hydrophobic surface treatment, the apparatus falls back into film condensation.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the operating condition: The starting quantities are the saturation temperature of the vapor and the wall temperature; their difference is the driving subcooling with which droplet nucleation and droplet growth proceed.
- Calculate the heat transfer coefficient of dropwise condensation: Using the empirical correlations of the VDI Heat Atlas, the heat transfer coefficient is determined as a function of saturation temperature and subcooling; it results from the interplay of nucleation at free sites, heat conduction through the growing droplets, and their roll-off cycle.
- Check the influence of the wall material: Because the heat is introduced into the wall locally beneath the droplets, a constriction resistance arises in the wall: with poorly conducting materials such as stainless steel, the effective heat transfer drops markedly compared with copper — the thermal conductivity of the tube therefore enters the calculation.
- Account for the inert gas influence: Non-condensable gases accumulate in front of the surface and throttle the vapor transport to the wall; even small inert gas contents massively reduce the high heat transfer of dropwise condensation and are captured via a dedicated reduction approach.
- Assess the result: The calculated heat transfer coefficient is fed into the overall heat transfer calculation; note that at such high condensation-side values, the coolant side, the wall, and fouling usually limit the overall heat transfer.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Saturation temperature | TS | K |
| Wall temperature | TW | K |
| Thermal conductivity tube | λ | W/(m·K) |
| Inert gas fraction | x | % |
| Temperaturdifferenz | ΔT a b | K (diff) |
| a | ΔT a b | - |
| b | ΔT a b | - |
| Wärmeübergangskoeffizient | α f(λ) | W/(m²·K) |
| Wärmestromdichte | α f(λ) | kW/m² |
| Material | α f(λ) | - |
| Material | αx/α0 | kW/m² |
| Wärmeübergangskoeffizienten | αx/α0 | - |
| Wärmestromdichte | αx/α0 | kW/m² |
| Wärmeübergangskoeffizient | αeff | W/(m²·K) |
Frequently asked questions
What determines whether dropwise or film condensation occurs?
The wettability of the surface: on bare metal surfaces, condensate generally wets completely and film condensation results. Dropwise condensation requires a hydrophobic surface — achieved with promoters (e.g. organic layers), polymer or DLC coatings, or noble metals such as gold. Technically, the long-term stability of these layers is the core problem: if they age or wear, the apparatus reverts to film condensation.
Why must a condenser usually still not be designed for dropwise condensation?
Because the condition cannot be guaranteed in operation: oil and dirt films, oxidation, and coating wear cause the hydrophobic treatment to fail over time. The design is therefore made conservatively for film condensation; the dropwise calculation serves as an assessment of the potential. Moreover, at α values of 100 kW/(m²·K) and more, the coolant side and the wall limit the overall heat transfer anyway.
How strongly does inert gas affect dropwise condensation?
More strongly than film condensation: since the condensation-side resistance is extremely small, the diffusion resistance of the gas layer dominates the process even at inert gas contents in the per-mille to low percent range and can lower the effective heat transfer by an order of magnitude. A clean vapor supply and degassing are therefore prerequisites for actually achieving the high coefficients.
What role does the wall material play in the heat transfer?
Beneath the individual droplets, heat enters the wall at point-like spots; within the wall, the heat flows must spread laterally. With highly conductive copper this constriction resistance is small, with stainless steel at around 15 W/(m·K) it is noticeable — measured heat transfer coefficients on stainless steel therefore lie well below those on copper, although the condensation process itself is identical.