Earth tube with Heat recovery in E+ or Design builder

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You are correct that the earth tube object in EnergyPlus is meant to be a standalone system that provides air directly to a zone. Most other HVAC components in EnergyPlus have inlet & outlet node settings that allow you to define where that component is located in the model, such as connecting the earth tube outlet air as the heat recovery inlet air. If you think that EnergyPlus should include this as a new feature, then you can make a comment in an existing feature request on Github where the EnergyPlus source code is hosted.

If you want to try a workaround, you could do the following:

1. Run an initial simulation with the earth tube object and report the Earth Tube Zone Inlet Air Temperature and Earth Tube Zone Inlet Wet Bulb Temperature that leaves the earth tube as hourly or timestep frequency output variables.
2. Create a modified EPW weather file that uses the air outputs from the first simulation as the outdoor air drybulb and wet-bulb. I would recommend using Elements to do this since it has psychrometric laws built in that prevent impossible air conditions (RH > 100%, e.g.).
3. Run a second simulation that removes the earth tube object, has the heat recovery device with outdoor air -> air intake on one path and extract air -> exhaust air on the other (using node names from your linked diagram), and uses your modified EPW file from the previous step. Now, the "outdoor air" drybulb and webulb entering the heat recovery device before supplying air to the zone is the same as what would have been leaving the earth tube.