When used at low flow rates, the airflow direction became opposite to the intended direction.

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I've made the change you indicated and tested with the latest release (22.1) and with my build of the in-development code. In both cases I am getting warnings, but the simulation completes. What EnergyPlus version are you using and what weather file? I wouldn't say my simulations are successful, there are 1000+ warnings about low flows and out-of-range temperatures, here's an example:

*************  ** Warning ** HeatExchanger:AirToAir:SensibleAndLatent "OA HEAT RECOVERY 1":  Average air volume flow rate is <50% or >130% warning continues. Air flow rate ratio statistics follow.
*************  **   ~~~   **   This error occurred 824 total times;
*************  **   ~~~   **   during Warmup 0 times;
*************  **   ~~~   **   during Sizing 0 times.
*************  **   ~~~   **   Max=0.115243  Min=0.115243

I would not expect such a drastic change of a single field to work very well, there's a lot that can go wrong with that, especially when you're changing one of the design inputs that's really likely to clash with other inputs. If you do go through the process of changing other inputs to silence all the warnings, you're likely to end up with a different design and that's probably not what you want. I'm guessing it would be better to limit the flow another way that doesn't change the overall design. Why are you interested in such a low flow rate?

Update

Looking at your file, I see that you have lowered the flow rate in more places than I did. That accounts for why mine completed and yours did not. It appears that the pressure solution is driving things backwards in a sense, and it may be that the pressures here are just not compatible with a simulation of the distribution system with such low flow. There are still other issues that could be playing a role. If I take the original example file and change the "AirflowNetwork Control" field in the AirflowNetwork:SimulationControl object from MultizoneWithDistribution to NoMultizoneOrDistribution, that simulation will complete and the only warnings are about unused AirflowNetwork objects being present and missing outputs. Both of those things make sense. If I take your file and do the same thing, I get a lot of warnings about low temperatures and such, so the HVAC is having a problem with the low flow rates. I also tried MultizoneWithoutDistribution with similar results.

So, what to do? I think there are two options:

1. If you can fix the warnings that are cropping up in the NoMultizoneOrDistribution simulation, then you can go back and try the AFN simulation and see what happens (with both MultizoneWithDistribution and MultizoneWithoutDistribution). Keep in mind that the distribution simulation may still not work, but the results are now at least more defensible. The handling of fans in AFN is necessarily somewhat simplified, and while it's possible there's a bug lurking in here somewhere, the distribution solution just may not be able to handle the low flows in this model.
2. If you take a look at the results of the MultizoneWithoutDistribution simulation of your current ...