Short Answer: I recommend applying as if it were the first time, do not mention that you are reapplying anywhere and do not worry if they find out. You can apply as often as you like (within reason) for as many positions at the company as you like (and are qualified for, or at least think you are qualified for). What to do with your applications becomes the HR dept's concern, not yours.
Long Answer, or things to keep in mind:
- The inner workings of the HR mechanism vary from company to company, and can even vary from one year to another at same company. This depends on company size, age (how set it is in its ways), economy (supply/demand), etc. For example, a company might decide to outsource its hiring functions, focusing internal HR on last steps of the process post-vetting, or more internal HR matters post-hire.
- There are many reasons applications are rejected. I say applications and not applicants -- there is a difference. A revised/improved application from the same person might be treated differently if they did a better job presenting themselves and illustrating a fit with the position and employer.
- As others have alluded, if the initial vetting is by a computerized system (more likely in a larger org), keywords are...well, key to passing that round. Study the job announcement carefully and pepper your resume with the right terminology where appropriate, without distorting the truth beyond what you could justify.
- Applications may be rejected due to factors outside of the applicant's control, i.e. things you are not responsible for. Examples: changes in budget may require cancelling a recruitment for a given position with a given department or unit. You might still feel rejected, but knowing that the reason may have nothing to do with you personally can help to get over that.
All this suggests that, unless you have insider knowledge as to specific reasons that led to the rejection on the grounds that have to do with YOU specifically, as a person, it is safe to assume the opposite. Conversely, even if it had something to do with you, this absolutely should not matter for your decision to reapply -- positions are posted to solicit applications from presumably qualified applicants. If you consider yourself to be one, go for it without a second thought.
Finally, a general advice: when applying for jobs, separate your emotions from the process. Treat applications as work on a conveyor belt at a sausage factory -- send them out the door and let them be. Don't get attached to the outcome of the application attempts -- let place, timing, and circumstances play out as they may. If you miss, simply move on. Also, if this helps, you can be sure that on the receiving end (especially at larger firms) your application is treated exactly this way -- as yet another sausage ;) You will not lose anything from maintaining such perspective, and will only gain patience, calmness, and will conserve valuable emotional and mental energy to be invested into other applications.
If all this sounds a bit dispassionate, that's the intent, because it should be when done right. I realize that your application is special and dear to you, and that you already imagine yourself in the position you are applying for and thinking of all the ways life will be better when you get it. And it's OK to allow yourself to do that - it makes the process way more fun!
At the same time, try to keep a cool head and don't dwell on the outcome in terms of what it means to your identity, future, happiness, etc. etc. Maybe you were rejected only to become available for a better opportunity around the corner. There is always something ele around the corner. Good luck!