Who uses ZoneMixing?

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As you've noted, ZoneMixing is for one-way flow of air in between zones. A few situations where you want to use this are:

1. Horizontal openings. ZoneMixing would represent the upward flow of air due to buoyancy, say in stacked zones that represent an atrium. You can read more details here.
2. Pressurization or depressurization. ZoneMixing would represent the intentional pressurization of supply air entering one zone, then "spilling over" into an adjacent zone (supply into an office and spill into an adjacent corridor) or the intentional depressurization of exhaust air leaving one zone and "pulling" air from an adjacent zone (exhaust from a restroom that pulls air from an adjacent corridor). You can read more details here.

Note that either mixing object you've mentioned is a "bulk airflow" added by the user -- EnergyPlus is "blindly" assigning an air flow to the model that may not be realistic. If you want to model internal air flow accurately, it would be better to use the Airflow Network feature where EnergyPlus calculates a proper air flow that should occur due to a pressure difference. Some drawbacks of this are there is overhead with defining detailed inputs of AFN objects, and it does increase simulation time.

UPDATE

TL;DR

If you're striving for the "perfect model" (if such a thing exists :) ), then AFN objects should be used to model airflow loads instead of "bulk airflow" objects like ZoneMixing.

Full Response

As you mentioned from the documentation, "bulk airflow" objects are really just "zone energy balance accounting" for the receiving zone only. They tell EnergyPlus that air moves within the model and there is a resulting sensible and latent heat exchange where the air flow ends up. They do not enforce energy balance where the air comes from (outdoors or the source zone).

I agree that this does not match reality.

Why would we use "bulk airflow" objects in general?

Because the alternative is the AFN objects, which comes with extra overhead of assigning very detailed inputs and longer simulation times for EnergyPlus to calculate air flows due to pressure differences. Not all energy modelers want to deal with that, and adding "bulk airflow" objects to models is better than doing nothing to account for air flow loads.

Why would we use the ZoneMixing object specifically?

Because users want to account for the impact of air moving between zones in one direction.

1. I should have clarified that the ZoneMixing object has simple control inputs for the user to specify limits on when the mixing air flow occurs. For the atrium example, that would be if the lower zone became hotter than the upper zone (air would flow upwards). In reality, you are correct that over time the hot air would naturally collect at the top of the atrium. However, EnergyPlus doesn't calculate this kind of fluid flow phenomena like a CFD tool would.

2. "If the corridor is not air-conditioned, normally we don't care about the air temperature of the corridor." While ...