In a case where I did a kitchen that had no venting options the insert had a short duct and there was a vent installed in a soffit that exhausted closer to the ceiling so at least it was not blowing out at the top of your head.

Install the duct. Recirculating hoods need ductwork tooI. You just exhaust the heat, odors, grease, steam, and smoke, inside the home, which is never good for indoor air quality.

@palimpsest yes a vent in a soffit sounds like it would fix the problem. Do you have photos? Is this something I would talk to my cabinet maker about or my electrician? And what brand of short duct was installed?
@verbo yes I agree. But it’s a condo with shared walls and hoa rules. Would love to have it vented but it’s not a current option.

I don't have any pictures, But it was a range hood insert that had a short duct which went up through a the cabinet above the hood and the turned and vented out the front of a soffit built above the cabinets. Be aware that this will stain the ceiling with a lot of use since it is discharging so close to it. I don't think that homeowner turned it on but rarely anyway. It was the same situation as yours, a condo situation and she could not have an exterior vent on the front of her unit.

@palimpsest oh I understand now. That makes sense. I don’t have a soffit above my cabinets because the ceiling is so low. The cabinets go right to the ceiling. So I still would have no where to vent the filtered air. 🤔hmmm

Review the information at Vent-a-Hood for their ARS series hoods for perspective on their air exit design. If embedding the filter exit in cabinetry, the vents in the cabinetry should be at least as large as those in the hood system. Larger would be better.

You could have a vent cover built into the cabinet door above the hood or you could blank out that area and have a matching wood panel with a vent in it.

Yes my electrician suggested that. I was just thinking ,visually, a vent in the cabinet front would be less than ideal. I’m wondering if maybe I can find a recirculating hood with a chimney that allows the air to exhaust out the sides of the chimney.

dancing queen the chimney hoods with side vents are very common...that would be my recommendation for you! Here's a ductfree chimney hood on one of my old 1990s displays. The brand was Sirius at the time. I'm not sure if they are still around.

Regarding the vent-a-hood ARS ductless that Kaseki cited above, they are expensive but the long running threads here are mostly favorable about their effectiveness. It definitely meets your criteria for a chimney with side vents up near the ceiling. If interested, you could start researching with this thread which started a decade ago and is still getting posts: https://www.houzz.com/discussions/2347276/vent-a-hood-ductless-ars-range-hood-update#n=164

Just installed this in a townhouse condo with no opportunity for exterior venting. We replaced an over the range micro. I have not cooked with it as of yet so can't speak to its effectiveness. Already warned the husband high heat searing will have to take place outdoors on the BBQ!

https://www.homedepot.com/p/Cosmo-30-in-Ductless-Wall-Mount-Range-Hood-in-Stainless-Steel-with-LED-Lighting-and-Carbon-Filter-Kit-for-Recirculating-COS-63175-DL/300862652

Thank you everyone! Yes I do think a recirculating hood with a chimney is my best bet. I just need to find one suitable for low ceilings so that the vents on the chimney can be utilized while maintaining a decent clearance between the hood and cooktop.