Optimizing Indoor Air Quality: Calculating Air Change Rate with Excel and MATLAB

HVAC air change rate is a measure of how many times the air in a room or space is completely removed and replaced in an hour. It is calculated by dividing the volumetric flow rate of air (in cubic feet per minute or liters per second) by the volume of the room or space (in cubic feet or cubic meters). The higher the air change rate, the more ventilation the room or space receives.

The air change rate can vary depending on the type and use of the room or space, as well as the outdoor air quality and the indoor air requirements. Different rooms and buildings may have different recommended or minimum air change rates to ensure adequate indoor air quality and comfort. For example, the ASHRAE 62.1 standard recommends that homes receive no less than 0.35 air changes per hour of outdoor air.

Basic Theory:

The basic formula for calculating Air Change Rate is:

$ACR = \frac{Q}{V}$

where:

$ACR$ is the Air Change Rate (in air changes per hour),
$Q$ is the volumetric flow rate of fresh air into the space (in cubic feet per hour), and
$V$ is the volume of the space (in cubic feet).

Procedures:

Determine the Volume of the Space (V):
Measure the length, width, and height of the space and use the formula:

$V = \text{Length} \times \text{Width} \times \text{Height}$
Determine the Volumetric Flow Rate (Q):
The volumetric flow rate is often specified by design standards or can be calculated based on the desired air
changes per hour and the volume of the space.

$Q = ACR \times V$
Excel Formulas:
Utilize Excel to perform these calculations. For instance, if the volume is in cell A1, the ACR in cell B1, you can
use the formula in cell C1:

$\text{C1:} = \frac{\text{B1} \times \text{A1}}{60}$

This assumes the ACR is entered as air changes per minute, hence the division by 60.

Real-world Scenario:

Let’s consider a conference room with dimensions:

Length: 30 feet
Width: 20 feet
Height: 10 feet
Desired ACR: 5 changes per hour.

Excel Calculation:

$V = 30 \times 20 \times 10 = 6000 \text{ cubic feet}$

$Q = 5 \times 6000 = 30000 \text{ cubic feet per hour}$

$\text{Excel Formula:} \quad =\frac{30000}{60} = 500 \text{ cubic feet per minute}$

Comparison with MATLAB:

For MATLAB, you can use similar equations, and here’s a simple script:

% MATLAB Script
length = 30;
width = 20;
height = 10;
ACR = 5;

V = length * width * height;
Q = ACR * V;
Q_per_minute = Q / 60;

disp(['Volume (V): ' num2str(V) ' cubic feet']);
disp(['Volumetric Flow Rate (Q): ' num2str(Q) ' cubic feet per hour']);
disp(['Volumetric Flow Rate per minute: ' num2str(Q_per_minute) ' cubic feet per minute']);

Result:

The Excel and MATLAB calculations should yield the same result, indicating the consistency of the computations.