Are there any organisations which approve or manage open science projects? Are there any organisations/foundations/hubs which manages/approve independent open science projects which are accepted and well recognised within mainstream scientific circles?

For instance, what if the published project doesn't make any sense and its calling it-self the open science project?

In other words, what kind of organisations/community ensure quality of the published data so it's accepted as reliable 'open science' project or anybody can publish anything and call it 'open science project' (for instance publishing open data of correlation of the number of pirates with global temperature)?
Yes, try looking at the Center for Open Science and their study management website, the Open Science Framework.  They primarily deal in psychology and cancer biology studies right now, but I'm sure other areas of science are welcome or will be soon.