Low air circulation in closet worried about smell

So my grow is 1 plant now but 2 later In a 4 ft high 4 foot wide closet in my kitchen. It has no place for exhaust except out front of closet. I Hang a black sheet over inside closet and seal it for total darkness I am 4 days into flowering. How much will just one plant stink with no legit exhaust? How cAn I eliminate or reduce the stank once it really starts to smell? My kitchen is right beside tv room and I'd rather not have the whole floor stink. Only have one fan blowing air in, no good space to blow air out and it wouldn't be good to blow all stank smell out across whole floor? I've read about carbon filters and other things like kitty litter in closet but I don't wanna spend alot would thosetime released air freshners do the trick if it's only one plant and I place it outside closet?

It's sweet tooth by the way. I was considering placing a CPU fan in top corner of closet entrance and hook up some kind of tube A few inches wide going out through curtain to ensure total darkness, wouldn't that just blow the stank out of closet into kitchen and tv room? Could I put a scrubber thing in tube to clean air as it blows out? Any suggestions will help first time growin here and this is only issue I can see myself having .... For now lol

if its a strong smelling strain, unlees it is vented or scrubbed properly, ur whole house is gonna smell really bad, trust me, been there...

There are a few really good threads here about making a DIY carbon filter. It is cheap and it is a really good way to remove a bunch of the odor out of the air and surrounding parts of the house.

So if I make a CPU fan carbon filter and put it in there it will reduce or eliminate smell, do I keep it in fully sealed closet or blowing out into the kitchen through closet?

its not going to work if the filter is stuck in the closet. drill a hole at the top right corner and tube it out underground or out a window.also remember if your sucking air out u might wanna keep the door alittle open or think of drilling another hole for the fresh air to get sucked in

If your strain is not a really strong smelling one, you could try getting by with a quart jar of ONA GEL opened up inside the closet. If you have a skunky, stinky plant variety, then you're gonna need a carbon filter of some kind. There are threads here where you can learn how to make a do-it-yourself version for way cheaper than buying one.