How to move air in and out without a vent. system?

Ok so I have a single autoflowering northern lights just planted in my closet, space is about 4x,1.5,x8, under 4 6500k, 23watt cfls at the moment. Temps are perfect I think, about 21-25C with the lights on 24/0, just waitin for her to pop outta the ground. So i still live with my parents(im 17 btw, not some 30 year old still livin at home and my rents know about my grow, theyre cool with it and all but dont want like a buncha ventilation stuff like ductwork and all that being done. So I was wondering if it would enough for the plant if I have the closet doors open and a 16" oscillating fan at the entrance of the closet? Also, about the smell, is there any way a carbon filter would work without it being attached to like duct work? I had this idea but it might be pretty stupid, i'm pretty baked right now.
Get a 5 gallon pail. fill it with activated carbon or whatever the recipe is for all that, and put holes all around the pail, then get a fan and put it on top of the pail so its sucking air in thru the holes, past the carbon, and blows out! or no....?

No the filter won't work nor do you really need one for one little auto, yes you will be fine just leaving it open with a little fan on it....you should not have said you are 17 your account will now likely be deleted...

Theoretically you could put a fan with a carbon filter into the closet to control smell. Not perfect as you are not sealing it. But with one plant, i think it would still suck up most odor before it got out. But it would be loud!

Phresh and Can Fan brand carbon filters are the most reputable brands. Get your filter from them at least.. you could get a fan from a different brand though... beware the fans can be pretty loud so you might consider getting a fan that is about 25% less powerful than the Fan/filter combo would suggest. I have not tried this but I have read on these forums that a 4" fan would be fine for filtering a 6" carbon filter because the slower air filtration gives more time for the air to make contact with the carbon. of course you would have to get a 4" to 6" ducting flange adapter. You can get these carbon filters and fans for less than $150... thats the safe way to go.

Ideally you want it connected to a sealed grow room. Make sure you have the fan pull the air through the filter and then exit... Stinky Air -> Filter -> Fan -> Clean air... ducting as necessary. you could go without ducting and stand the carbon filter and have the fan on top of it sucking air through filter and blowing it upwards. Either that or use ducting to have the air blow out near your doorway so clean air is at your doorway. This should filter a majority of the smell... without a sealed grow room it is going to be difficult to completely have things under control.

Other things you will want as soon as possible..

Sealed grow room or tent (as low as 50 bucks)

250 or 400 watt High pressure sodium Lamp, Ballast, and Reflector... as low as $100... depends on which grow room size you are using... you could probably get some orca film or panda film and line your closet. (less than 50 bucks i would imagine) and find a way to get a zipper or velco door to enter... On the top to the side of the doorway you should make a hole big enough to insert ducting and reinforce so the plastic doesnt tear. on the sides out of the way of the door make another hole slightly larger than the hole near the top. Put some carbon prefilter here to keep light, bugs, and dirt out of your grow environment.

$250 bucks and a little DIY.. Better to go with the true and tested methods... there is a reason so many people use HIDs, grow tents, and carbon filters... they are the core of having a successful and odor controlled grow on a budget.