Correct minor factual error in docs: evaporative-coolers.tex

[Preposthumous]

General Summary

This issue requests a correction in documentation, only. It appears that the program, itself, is performing calculations correctly. (...but perhaps for the wrong reason?)

Detailed Description

In doc/engineering-reference/src/simulation-models-encyclopedic-reference-002/evaporative-coolers.tex, circa line 15, the documentation currently reads:

The thermodynamic process is a simultaneous heat and mass transfer, or adiabatic cooling, and follows a constant enthalpy line on the psychrometric chart; it is shown in the figure below as a process from A to B. Since the deviation of the constant wet-bulb line and the constant enthalpy line is small, it is assumed that the wet-bulb temperature is constant across the direct evaporative stage.

This is incorrect. Specifically, an evaporative cooling process should NOT follow a line of constant enthalpy on a psychrometric chart, and a constant wet bulb line is NOT merely an acceptable proxy because of its small deviation from the lines of constant enthalpy. I would suggest that this passage should read something more like:

The thermodynamic process is a simultaneous heat and mass transfer. The process is adiabatic; the enthalpy of the air leaving the cooler will be equal to the sum of the enthalpies of the air entering the cooler and of the evaporating liquid water before it evaporates. On the psychrometric chart, evaporative cooling processes do not follow lines of constant enthalpy because the starting and ending moist air enthalpies should differ slightly to account for the liquid water's enthalpy pre-evaporation.

Instead, an evaporative cooling process follows a constant wet bulb temperature line on the psychrometric chart. This is because this exact kind of evaporative cooling is the basis for the definition of "wet bulb temperature." An example is shown in the figure below as a process from A to B.

In most contexts that matter in our field, the difference between "constant wet bulb" and "constant enthalpy" on a psych chart won't change the design selection outcome of a calculation if you're using sig figs right. However, having personally written private calculation tools that compare the two results, I can report that this can make a difference on the order of a couple percentage points in projected annual water usage near sea level, with more profound differences at higher elevations and in drier climates.

Possible Implementation

If, for some reason, an equation would help illustrate the explanation, I think this one follows the document's notational conventions:

\begin{equation}
{h_{sup,out}} = {h_{sup,in}} + {h_{water}} * \left( {{w_{sup,out}} - {w_{sup,in}}} \right)
\end{equation}

Where:

\({h_{sup,out}}\) is the specific enthalpy of the moist air leaving the direct evaporative cooler (J/kg\({_{dry \, air}}\))

\({h_{sup,in}}\) is the specific enthalpy of the moist air entering the direct evaporative cooler (J/kg\({_{dry \, air}}\))

\({h_{water}}\) is the specific enthalpy of the liquid water being evaporated (J/kg\({_{water\,liquid}}\))

\({w_{sup,out}}\) is the humidity ratio of the air leaving the direct evaporative cooler (kg\({_{water\,vapor}}\)/kg\({_{dry \, air}}\))

\({w_{sup,in}}\) is the humidity ratio of the air entering the direct evaporative cooler (kg\({_{water\,vapor}}\)/kg\({_{dry \, air}}\))

... but that's probably unnecessary.