I do not understand what your problem is.
That is a standard Kawakasi air filter currently fitted to the domestic range
IT is a bad design as over tightening the clamp between the rubber elbow & the filter deforms the filter spigot causing an unfiltered air leak.
In use air from the cooling fan is forced into the housing so in theory it gets it's air from the top of the engine and if your mower has an air scoop and cowl under the bonnet then clean air from the top of the hood .
I come up with the part number 11013-0752 same as Scrubbie did
IMHO the best thing to do with these filters is toss them away & fit the canister style Donaldson ( as fitted on the FX series )
The only time I have seen massive dust problems was with the 110130752 filter fitted to ZTR's with baggers because the customer did the clamp up too tight .
i've concluded we're getting the run-around with this style of filter . HOW ? these type filters will work on any riding lawn tractor or engine . The requirements are it will go into the compartment of that design , the hose ends will fit as designed and the shroud cover will re-install . The cover --- it looks to me it was made to draw atmospheric air across the carburetor on its way to the filter .
