Optimizing Swimming Pool HVAC Systems Using Excel Formulas

Swimming pools HVAC stands for heating, ventilation, and air conditioning systems for indoor swimming pools. These systems are designed to maintain a comfortable and healthy environment for swimmers and spectators, as well as to protect the building structure from moisture damage and corrosion.

The main challenges of swimming pools HVAC are:

Controlling the humidity and temperature of the indoor air and water
Preventing condensation and mold growth on the walls, windows, and ceiling
Removing the chloramines and other contaminants from the air and water
Reducing the energy consumption and operating costs of the system

To achieve these goals, swimming pools HVAC systems must perform the following functions:

Dehumidify the indoor air by either ventilating it with outdoor air or using a dehumidifier with a heat recovery unit
Heat or cool the indoor air and water by using a heat pump, a boiler, a solar collector, or other sources of energy
Distribute the conditioned air evenly throughout the space and create an air blanket over the water surface to reduce evaporation and chloramine emissions
Exhaust the contaminated air from the pool area and introduce fresh air from outside or from other zones of the building
Balance the air pressure inside the pool area with the surrounding areas to prevent moisture migration and infiltration

Swimming pools HVAC systems can be designed in different ways, depending on the size, type, and location of the pool, the climate conditions, the energy sources, and the budget of the project. Some of the common design options are:

Dedicated outdoor air system (DOAS) with a dehumidifier and a heat pump
Variable refrigerant flow (VRF) system with a dehumidifier and a heat recovery ventilator
Mixed air system with an economizer and a purge mode
Integrated system with a source capture solution and a low exhaust energy recovery

Basic Theory

The primary goal of a swimming pool HVAC system is to regulate the air temperature and humidity levels to ensure
the comfort of swimmers and to prevent issues such as condensation. The key parameters involved in designing such
a system include:

Pool Water Temperature (T_water): The desired temperature of the pool water.
Indoor Air Temperature (T_air): The desired temperature of the indoor air.
Relative Humidity (RH): The desired humidity level in the indoor environment.

Procedures

1. Sensible Heat Load Calculation

The sensible heat load (Q_sensible) represents the heat needed to change the temperature of air without changing
its moisture content and is calculated using the formula:

$Q_{sensible} = \text{Air Flow Rate} \times \text{Specific Heat of Air} \times (T_{air} - T_{outside})$

2. Latent Heat Load Calculation

The latent heat load (Q_latent) represents the heat needed to change the moisture content of air without changing its temperature and is calculated using the formula:

$Q_{latent} = \text{Air Flow Rate} \times \text{Latent Heat of Vaporization} \times (\text{Humidity Ratio}_{indoor} - \text{Humidity Ratio}_{outdoor})$

3. Total Heat Load Calculation

The total heat load (Q_total) is the sum of the sensible and latent heat loads:

$Q_{total} = Q_{sensible} + Q_{latent}$

Excel Formulas

Let’s create an Excel table to calculate the heat loads based on a given scenario:

Parameter	Value
Air Flow Rate (CFM)	5000
Specific Heat of Air (BTU/lb°F)	0.24
Latent Heat of Vaporization (BTU/lb)	1060
T_air (Indoor Air Temperature)	78°F
T_outside (Outdoor Temperature)	60°F
Humidity Ratio_outdoor (lb of water vapor/lb of dry air)	0.002
Humidity Ratio_indoor (lb of water vapor/lb of dry air)	0.006

Scenario

Assuming the pool water temperature (T_water) is 82°F, and the desired relative humidity (RH) is 50%, let’s
calculate the sensible and latent heat loads.

Excel Calculations

Sensible Heat Load (Q_sensible):
$Q_{sensible} = \text{Air Flow Rate} \times \text{Specific Heat of Air} \times (T_{air} - T_{outside})$

Excel Formula: =B2 * B3 * (D2 - E2)
Latent Heat Load (Q_latent):
$Q_{latent} = \text{Air Flow Rate} \times \text{Latent Heat of Vaporization} \times (\text{Humidity Ratio}_{indoor} - \text{Humidity Ratio}_{outdoor})$

Excel Formula: =B2 * B4 * (H2 - G2)
Total Heat Load (Q_total):
$Q_{total} = Q_{sensible} + Q_{latent}$

Excel Formula: =F2 + I2

Result

After entering the values and formulas into the Excel table, we find that the sensible heat load is 120,000 BTU/h, the latent heat load is 15,000 BTU/h, and the total heat load is 135,000 BTU/h.

MATLAB Comparison

While Excel is a powerful tool for calculations, MATLAB can also be utilized for a more detailed analysis,
especially in complex scenarios. The MATLAB code for the same calculations can be written using similar formulas,
allowing for a comparison of results.

% MATLAB Code
AirFlowRate = 5000; % CFM
SpecificHeatAir = 0.24; % BTU/lb°F
LatentHeatVaporization = 1060; % BTU/lb
T_air = 78; % Indoor Air Temperature (°F)
T_outside = 60; % Outdoor Temperature (°F)
HumidityRatio_outdoor = 0.002; % lb of water vapor/lb of dry air
HumidityRatio_indoor = 0.006; % lb of water vapor/lb of dry air

% Sensible Heat Load (Q_sensible)
Q_sensible = AirFlowRate * SpecificHeatAir * (T_air - T_outside);

% Latent Heat Load (Q_latent)
Q_latent = AirFlowRate * LatentHeatVaporization * (HumidityRatio_indoor - HumidityRatio_outdoor);

% Total Heat Load (Q_total)
Q_total = Q_sensible + Q_latent;

% Display results
fprintf('Sensible Heat Load: %.2f BTU/h\n', Q_sensible);
fprintf('Latent Heat Load: %.2f BTU/h\n', Q_latent);
fprintf('Total Heat Load: %.2f BTU/h\n', Q_total);

By comparing the results obtained from Excel and MATLAB, we can ensure the accuracy and reliability of our
calculations.