**Using “Mean Age of Air” in CFD Analysis**

*Characterizing Transient Behavior with a Steady State Solution*

By Kelly Hile

The “Mean Age of Air” is a concept that finds its roots in the HVAC industry. In designing a building airflow system, an HVAC professional looks at the exchange rate of a room, a measure of how quickly the room air is evacuated when the supply/return air flow engages. Ideally, multiple “air changes” would take place per hour, with higher rates depending on the type of space, be it warehouse, office, or laboratory. The exchange rate is determined through a basic handbook calculation that takes the flow rate divided by the volume of the room. This value might be useful for general comparisons, but the oversimplification does not account for room geometry, stagnation zones, or short-circuiting flow patterns. The Mean Age of Air helps to shed some light on these issues.

## What is the mean age of air?

**Mean Age of Air: The average time it takes for air to travel from a supply inlet to any location in a ventilated space **

The mean age of air was originally intended as an experimental measurement. The idea is to introduce a tracer gas into the supply air of an enclosed room, and then measure how long it takes for the gas to reach a given location in the room. Alternatively, a “step down” approach is to fill the room with tracer gas, and measure the time it takes for the tracer gas to dissipate. Mathematically speaking, the mean age of air could be described as the area under the concentration curve of the tracer gas, divided by the initial tracer concentration.

## Modeling Mean Age of Air

The experimental results give an idea of what’s happening throughout a room, in a way that accounts for imperfect mixing of room air. In lieu of experimental data, a transient CFD simulation could offer a similar analysis, where a tracer gas is “introduced” as a source term into each cell of the model space at time zero. The fluid dynamics of the room can then be analyzed to calculate the mean age of air as described by the above equation, integrating under the concentration curve over time.

Given the size and number of data sets required, the process of determining mean age of air for a transient simulation can grow cumbersome. The good news is that the steady state solution contains everything needed to calculate the mean age of air at any location in the model! A steady-state solution has already characterized the primary and secondary flow structures, or the convective and diffusive factors in flow behavior. Because of this, a steady-state simulation can be leveraged to predict some of the transient behavior of the fluid, including the mean age of air.

Here’s how it works. First, the user defines a mass fraction scalar field to represent the tracer gas. A source term of the “tracer” is introduced to each cell of the model, mimicking the “step down” approach in the age of air experiments. The inlet to the system must have a mass fraction of zero, to represent clean air entering the space. When the source term is equal to the density of air, the resulting final mass fraction in that cell is the Mean Age of Air in seconds. The steady-state Mean Age of Air is very consistent with transient analysis of the same flow system.

### Setting up Mean Age of Air in Steady-State

- Add a scalar field to the solution representing the tracer (a mass fraction field)
- Set a mass fraction source term in each cell that equals the density of the fluid in that cell
- Set the inlet boundary conditions of the scalar field to zero, representing “clean air” entering the space
- The resulting scalar field value represents time, or the mean age of air at that cell location in seconds

Beyond HVAC, the Mean Age of Air concept can be applied to other enclosed spaces as well, such as residence time of a reactor, the effectiveness of a mixing process, or the average time required for thorough cleaning or purging of a storage tank.

## Additional Resources

For a deeper dive into Mean Age of Air, watch this online training session with Azore lead developer, Dr. Jeff Franklin. This session features case studies and comparisons between steady-state and transient simulations, plus insight on creating transient-like animations with steady state data. Animations of Mean Age of Air are simple to create in Azore, using iso-surfaces that can be easily generated in post.

For a real-world example of CFD modeling for indoor airflow, check out this simulation of a school classroom, which compares the handbook exchange rate to the Mean Age of Air in all locations of the room.

Airflow Sciences Corporation performs age of air analysis services. Learn more about their work in the HVAC industry here.

Eager to get started with modeling the mean age of air? Watch the step-by-step tutorial for Mean Age of Air setup in Azore.