The thermal design of wet cooling towers still rests largely on Merkel's 1925 work [1]. Merkel reduced the combined heat and mass transfer in air-water systems to a single transfer process driven by the enthalpy difference. That reduction made the problem solvable by hand, which is why the method has survived for a century.
The three assumptions it rests on
- The Lewis factor is taken as 1 — the relationship between the heat and mass transfer coefficients is treated as constant.
- Evaporated water is neglected in the energy balance — the reduction in water flow rate is not accounted for.
- The exiting air is assumed saturated and characterised only by its enthalpy.
Kloppers and Kröger compare the Merkel, Poppe and e-NTU methods and show where and by how much these assumptions distort the result [2]. The more detailed approach of Poppe and Rögener drops the saturation assumption and solves for the true state of the exiting air.
In practice the difference matters here: if the amount of water evaporated has to be known accurately — water consumption, discharge load, salt accumulation — Merkel is not sufficient.
What CFD adds to a tower
Merkel and its descendants are a fill performance calculation, and the fill characteristic comes from experiment. Where CFD belongs is in what that calculation assumes but the site does not deliver:
Distribution. The calculation assumes air and water are distributed evenly over the fill. In reality the fan inlet, drift eliminators and structural members disturb it. Most of the unexplained loss in tower performance lives here.
Recirculation. Warm, humid air leaving the tower finds its way back to the intake. Because it raises the wet-bulb temperature this is a direct performance loss, and it depends on the site layout, wind direction and neighbouring structures — none of which is visible without modelling the outdoor environment.
Drift. Droplets carried off by the air stream; important for environmental and corrosion reasons. This is a particle tracking problem.
Winter conditions. Freezing and ice formation begin where the distribution is weakest; a mean calculation will not show that.
A modelling note
Resolving the fill cell by cell is neither possible nor necessary; the fill is represented as a porous region with a known resistance and enthalpy transfer characteristic. The accuracy gained lies not inside the fill but in how the fill is approached.
Results should be compared against an accepted performance test, and if the measurement uncertainty is ignored the agreement will be a coincidence. See the verification and validation note.
References
- Merkel, F. (1925). Verdunstungskühlung. VDI-Forschungsarbeiten No. 275, VDI-Verlag, Berlin.
- Kloppers, J. C. & Kröger, D. G. (2005). Cooling tower performance evaluation: Merkel, Poppe, and e-NTU methods of analysis. Journal of Engineering for Gas Turbines and Power, 127(1), 1–7. DOI: 10.1115/1.1787504