The inks used in a normal inkjet printer are water based. They cannot be dissolved in turpentine.
A water based cleaner is needed, for instance water + an alcohol + a glycol + a little ammonia as in "pharmacist's cleaning solution". Many window cleaners have similar contents and are also suitable as print head cleaners.
Special solvent based inks are used in some industrial printers and need special solvent based cleaners, but that is another story.