"just circulated" is correct and usable in written English.
You can use it to refer to when something has recently been sent out or spread around. For example: "The new company policy just circulated to all employees."
The relatively liberal People's Bank of China (PBOC) has just circulated a study that recommends opening up the financial system, with a ten-year timetable for easing capital restrictions.
The reports come at a sensitive time diplomatically, as the UK has just circulated a draft resolution at the UN Security Council which would open the door for military intervention.
Nurses rigged up fans at patients' bedsides, but with the windows closed tight they just circulated hot air.
See if it can economically be purified by something like activated carbon, or might be neutralized rather than just circulated by an air conditioner (whose condensate may absorb odour and is generally sent outside) or furnace (whose heat might destroy it), in which case changing baby by a convenient intake could be acceptable.
You only get power through tips of blades, just circulating in space.
"They're happy when you just circulate, grabbing garbage," like dirty cups and cocktail napkins.
If you get inulin in your blood, it just circulates and isn't changed at all, but it's small enough that it's filtered in the glomerulus.
It would also apply to vehicles even when they are not carrying passengers to discourage drivers from just circulating around Manhattan streets looking for business.
"If there are no windows or doors open you're just circulating the hot air".
And instead of just circulating posters on 4Chan and Reddit, there would have been a big campaign by Anonymous to take on Lulzsec".
