1. Introduction

Cooling and humidification is a very common process in HVAC. In this post, we are going to see how to implement calculations for cooling and humidification in Excel.

To do so, we are going to use the psychrometric add-in you can download from here:

https://wcec.ucdavis.edu/resources/software-resource-applications/

You may be also interested in plotting the psychrometric chart as we discussed in our post:

https://www.pharmaceuticalhvac.com/a-psychrometric-chart-in-excel/

In particular, this is the cooling and dehumidification process that we are going to study:

It consists of the mixing of fresh air (OA) with the room return (RM). The new point will have the characteristics of the MA point.

After the mixing, the air passes through the cooling coil, cooling the air close to the dew point to produce the condensation. Finally, we will consider the fan heating effect and if necessary, reheating to increase the air temperature to the supply temperature and humidity conditions to remove the generated heat (latent and sensible) in the space. As usual in pharmaceutical systems, supply airflow will be constant.

2. Input Data

The first data we have to input are:

• Site location (and height), to calculate the barometric pressure
• Outdoor conditions, temperature and relative humidity (or wet bulb temperature)
• Indoor conditions, temperature and relative humidity (or wet bulb temperature)

2.1. Site location

In cell C7 we put the STD_Press related to C6. Here we obtain the barometric pressure at the height site.

2.2. Outdoor and Indoor conditions

Other inputs we need are (cells in blue):

• Outdoor temperature and relative humidity
• Indoor temperature and relative humidity

In our last post https://www.pharmaceuticalhvac.com/determining-outdoor-design-conditions/, we discussed how to import climatic data into excel.

With this data, we can calculate the outdoor and indoor air density and absolute humidity, that we will need later on (Dry_Air_Density and hum_rat2 functions).

2.3. Airflow

Here we can calculate the necessary airflow, as described in our posts, About Air Changes, and Cleanroom Air Balance.

In the example below, it is manually written, but you can link to the result of the calculation based on the air changes:

The recirculation ratio is the recirculated airflow divided by the total supply airflow.

2.4. Heat gains

The following input we need to know for our cooling and dehumidification in Excel calculations are the heat gains. An explanation of this topic you can find in our post Heat Gains. That means the heat we have to remove from our space, sensible and latent. It is very important to know the sensible heat factor, that is the sensible heat part, divided by the total heat (sensible + latent).

In this example, we have put manual values, but you could link them from the results of your calc sheet.

3. Calculations

Arrived at this point we have all the necessary data to start with the calculations. These will be:

• Air mixing temperature
• Air supply temperature
• Air mixing humidity
• Fan power
• Psychrometric characteristics (enthalpy, dew point, air density) for each point (outdoor, indoor, mixing, cooling,…)
• Sensible Heat Ratio Slope
• Cooling coil exit Humidity
• Apparatus dew point
• Cooling capacity
• Reheating capacity
• Condensation capacity
• Coil exit conditions based on the bypass factor
• Outdoor conditions, temperature and relative humidity (or wet bulb temperature)
• Indoor conditions, temperature and relative humidity (or wet bulb temperature)

3.1. Air Mixing Temperature

To calculate the air mixing temperature we will use the following formula:

Then:

3.2. Air supply Temperature

Afterwards, we will calculate the air supply temperature for the selected airflow. We will use the following formula:

Translated into Excel:

3.3. Air Mixing Humidity

Now it’s the turn of air mixing humidity calculation. We will use the following formula:

We can start to arrange the complete psychrometric characteristics for each point, that we will use later:

3.4. Fan Power

We will need to estimate the fan power to calculate the temperature increase by passing through it. This formula can give us a good approximation for the real value:

Thus, in our example, for a typical cleanroom fan of 1300 Pa static pressure and an efficiency of 79%, we can calculate an approximate motor of 11.6 kW:

Moreover, we can know the increase in temperature due to the fan.

In our example, the increase of temperature is 2.1 °C:

3.5. Psychrometric points

For each point, we will tabulate the enthalpy, the air density, dew point, etc, with the aid of the psychrometric functions. In the caption below we can see the procedure for the air mixing point:

3.6. Sensible Heat Ratio Slope

Now we need to calculate the slope of the room sensible heat ratio (SHR). This slope will allow us to know how the room humidity increases with the temperature, and thus to determine the humidity condition at the cooling coil exit. For that, we will use the SHR in this enthalpy format:

You will note that the SHR slope is not linear with the temperature. But we can consider it constant in the range from supply temperature, and room temperature. This will not affect the final result.

3.7. Humidity target

Right now we can calculate the humidity we need to achieve to satisfy:

• The dehumidification of the inlet air (in our example, the mixed air)
• The foreseen increase of humidity due to the latent loads, to maintain the room conditions at the desired point

As we have one known point (room temperature & humidity), one slope (room sensible heat ratio calculated in the previous section), and one point which we know the temperature (supply), we can deduce the humidity in the air supply stream (target humidity) by means of the point-slope equation:

3.8. Apparatus Dew Point Temperature Iteration

Thereupon we have to calculate the apparatus dew point (ADP) that satisfies the humidity target, based on the coil bypass factor, coil inlet humidity (air mixing in our example), and considering that the ADP will be located in the 100% RH line by definition.

To do so, we will use a module that you can download from here:

The iteration procedure is the following:

1. Guess an Apparatus Dew Point Temperature (Tadp)
2. Calculate the saturation pressure at Tadp
3. Calculate the coil humidity at Tadp and P (site barometric pressure)
4. Calculate the coil humidity exit based on humidity in, Bypass factor and coil humidity at Tadp
5. Now compare this calculated coil exit humidity with the target.
6. Is this lower than the target? Then guess another Tadp by adding 0.1 °C
7. The iteration loop is repeated until the calculated humidity matches the target

Just go to the option developer in Excel (be careful, it’s not activated by default) and press “Visual Basic” option. A new window will be open, the “Microsoft Visual Basic for Applications”. Then press “Insert” and “Module” in the submenu.

In the edition field, you can paste the code for Tadp function mentioned above.

Thereafter we can go to the calculation of the cooling coil apparatus dew point by selecting the new programmed function Tadp. You should press the button fx and look in the “user defined” section to find it. The inputs we need to fill in are the target humidity calculated in the previous section, the site barometric pressure, the humidity entering the coil, and the bypass factor.

The bypass factor is defined as the percentage of air that does not touch any coil surface. Therefore, for dehumidification applications, we should choose a cooling coil with a low bypass factor. Values between 0.05 and 0.15 are commonly applied.

The relative humidity for the apparatus dew point, by definition, will be 100%.

3.9. Cooling capacity

We will calculate the cooling capacity as the difference of enthalpies between the air conditions entering and exiting the coil. To know the exit enthalpy we need to know the coil exit temperature. But this is not complicated with the apparatus dew point temperature. The cooling coil path can be approximated as a straight line between the air mix point and apparatus dew point. Please note that this is an approximation. The real performance of a cooling coil is a curve, but for our calculation purpose, this approximation is quite good. The cooling coil exit temperature will be located within this line. How far or close to the saturation point depends on the bypass factor.

Later, knowing the temperature and absolute humidity, we can calculate the remaining psychrometric characteristics:

The enthalpy is:

And by using the cooling capacity formula:

3.10. Reheating Capacity

Normally, in the dehumidification process, we have to low down too much the exit temperature coil to condensate the moisture excess. If the calculated supply temperature to compensate the room sensible heat is higher than the coil temperature, we will need to reheat.

Additionally, if the fan is located after the coils (recommended in dehumidification processes), we can use this generated heat to save reheating coil capacity. But this is up to you.

The reheating capacity is calculated based on the difference of enthalpies, by using the same formula we used for cooling capacity.

Moreover, is a good practice to double-check that the calculated fan power matches the guessed one:

3.11. Water condensation

Lastly, we are going to calculate the water condensation that shall be collected by the drain pan and the condensation piping. We will use the following formula:

4. Conclusions

I would not finish this post without a manual checking of the calculations here shown. So I plotted all the points and I saw that the results are satisfactory and pretty accurate. The enthalpies and other variables confirm the calculated values. Furthermore, the slope of the Room Sensible Heat Ratio matches the protractor. The barometric pressure difference from our example and the chart at 0 meters sea level is negligible.

I always recommend plotting the psychrometric process to visually check that everything is in order. For example, a common mistake is to draw a cooling coil line to a coil exit RH less than 80%. In that case, condensation will never occur.

Instead of plotting manually, you can use Excel as well to represent graphically the psychrometric chart. This is described in our post A Psychrometric Chart in Excel