Air-Change-Per-Hour to Maximum Air Flow Rate Equation
(Air) infiltration in buildings is commonly used to denote the thermal interaction of conditioned indoor air with the unconditioned outside air through bidirectional and dynamic air mass exchanges. Simply put infiltration is either leakage of cool indoor air to the outside environment (~exfiltration) or penetration of cold outside air to the indoor environment (~infiltration). This thermal interaction is dynamic as it changes its directionality based on the relative differences of the temperatures of inside and outside air and this interaction is uncontrolled or in a sense unintentional and the exchanges take place through sections of the building’s thermal envelope which is in direct contact with the ambient conditions. Exterior windows and skylights (and especially the operable ones), doors (at main entrances and loading dock doors), and any type of openings or penetrations through the continuous building envelope (mechanical electrical system conduits) are the sections where air infiltration commonly takes place.
Air infiltration is inherently unintentional during building’s operation since the magnitude (and the rate) of air exchange is related to architectural design, detailing and construction quality of the building sections (windows, doors, envelope openings) that induce the exchange under varying environmental stresses. Infiltration is directly related to how airtight the building assemblies are to resist against the air flows that can happen even at millimetric scales between joints, frames, dividers and linkage elements. Air pressure differences between inside and outside air that are either originated by buoyancy effects (due to height) and wind forces (of the climate) are the main physical driving mechanisms for the air infiltration. Building sections are just the means but they can impact the rate of flow under given potential difference (~that is the air pressure difference in this case). That is why infiltration levels are most of the time indicated at certain pressure differential between inside and outside.
The big question is when it comes to including infiltration effects into your building energy model is how to quantify the amount of air that will leak into or outside of a building during its operation. One of the common metrics of this quantification is the Air Change Per Hour or “ACH” in short. ACH simply indicates how much of the indoor air volume is exchanged with outside air volume in an hour of time period due to infiltration effect. Therefore, if a given building space has an ACH of 0.75 this means that 75% of the total indoor air volume is completely exchanged with outside air in a single hour. Think about it for second. About 75% of your warmed or cooled, humidified or dehumidified (simply conditioned) indoor air will be totally replaced with outside air which is most probably at conditions that is not conducive to the required indoor thermal comfort levels and which needs to be taken care of (conditioned) at some point. And this thermal care is most of the time given by the HVAC systems since infiltrated cold air for instance will naturally lower the indoor air temperature and this will consequently trigger the operation of heating system to push more warm air to the space to combat this negative thermal effect. Thus, air infiltration can become a significant portion of the heating or cooling load of a space and a system serving the space incase the envelope is leaky and not airtight at all.
Going back to ACH, it is so clear that the greater the ACH the greater the volume and rate of unconditioned outdoor air flow to the building spaces. Below are some typical assumptions of different ACH characterizations.
0.10 ACH – Very tight envelope (like a Passive House PHIUS certified one)
0.33 ACH – A tight contemporary envelope (typical assumption for the DOE’s reference buildings)
0.50 ACH – A fairly tight envelope
1.00 ACH – Leaky envelope
1.50 ACH – Recently built leaky envelope
2.00 ACH – Very leaky and problematic envelope (an existing building that needs a retrofit)
Air infiltration can be characterized by the overall volume based ACH method (air change method) or it can also be given as an air flow rate (Q) in unit time. We can talk about Q as the maximum air flow rate per thermal zone or we can go one step ahead and define Q per unit surface area. But the immediate question would be the surface area of what? There are two approaches the first one (and the most common one) is QS which is the max air flow rate per surface area of exterior walls and the second approach is the QF which is the max air floe rate per surface area of thermal zone’s floor area. Now, how can we go from ACH to calculate Q, QS, and QF? Below is the answer which states the conversion of ACH to max air flow rate metrics.
I: Infiltration Rate expressed (1/hr or ACH)
V: Volume of the thermal zone (m^3)
F: Floor area (m^2)
S: Exterior wall area (m^2)
Q: Maximum air flow rate (due to infiltration) (m^3/s) (L/s)
QF: Maximum air flow rate per floor area (m^3/s.m^2) (L/s.m^2)
QS: Maximum air flow rate per exterior wall area (m^3/s.m^2) (L/s.m^2)
We can find Q by just multiplying the ACH with the volume of the thermal zone and divide it by 3600 to convert hour to second since Q is a flow rate per sec with a unit of measurement of m^3/s or CFM in IP system.
To represent Q as Liters/sec (L/S) just multiply it by 1,000.
Below is the equation for the maximum air flow rate density per floor area (QF). What we do here is to divide the Q by the floor area of the thermal zone. It is just like a normalized air flow rate per floor area.
Below is the equation for the maximum air flow rate density per exterior wall area (QS). There is also a division by surface area here but this time it is the surface area of “exterior walls” of the thermal zone.
QF and QS have the same units of measurements, but their actual values would be different for the same space. I find it useful to emphasize that Q terms are tied to the thermal zone geometry which means that starting with the same ACH of 0.33 for example, you would end up with totally different Q terms as you change the building hence thermal zone geometry. Any change in zone volume, floor area or exposed wall area will change the Q terms. Sometimes, users need to pick which input type would be preserved (unchanged) when a thermal zone geometry is updated. Best approach is to preserve ACH (1/hr) and let the others alter as zone geometry is updated. However, during later stages of modeling in case some standard values of air flow rate per areas are being used to infiltration rate inputs then let ACH become dynamic. Below is typical input screen from the IESVE 2021 program (Apache Module).
In this example, I entered the values of 0.33 ACH (1/hr) to indicate a tight contemporary envelope construction’s infiltration rate characteristic and click on it to put the asterisk (*) so that ACH input will be preserved in case thermal zone geometry is updated. Meanwhile, IESVE program automatically calculates the Q-terms (Q, QF, and QS) based on the thermal zone geometry. IESVE even calculated QP which is the max air flow rate per person in the thermal zone. This is basically dividing the Q by the peak number of occupants in the thermal zone.
Now that we have the first introduction to the air infiltration and some modeling basics, we can ask further questions and dig deeper into this topic. During future discussions on the same topic we’ll be looking at some detailed points such as measuring the infiltration rate, positive pressurization of the HVAC systems, temporal profiling/scheduling of the infiltration rates, infiltration inputs for interior/core thermal zones, and also how to deal with ASHRAE Standard 90.1-2016 Appendix G Section G3.1.5b instructions so that we can model standard compliant infiltration levels (which should be exactly the same for your baseline and proposed building models).
Omer T. Karaguzel, PhD
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