I write the beginner perspective on criterium races. In my most recent one, I got clipped and went down on a turn at about 22 mph. I scraped my hands, arms, hip, and shoulder. It's 8 days later and my dressings are all off and the skin is all closed. Here's what I did.
Get the wound cleaned up. Soap and water is best. Avoid hydrogen peroxide except for the initial cleaning as it kills the good stuff that heals your wounds as well as the bed stuff that infects it. And if you do use hydrogen peroxide, it needs to be rinsed with water after.
Bacitracin or some double antibiotic ointment LIBERALLY applied to the wound, especially after bathing. Initially, the bathing hurts, some times a lot, but it gets better as the skin heals.
After applying the ointment, cover the wound with telfa. Telfa is a non-stick dressing that will not peel away your healing skin when you remove it. You can also remove it in the shower after getting it wet if necessary.
Apply tape around the edges or wrap with a roll-up type of gauze such as conform or kerlex. You can also use an ace wrap. I prefer to use tape.
For the knee, a combination of tape and a 6" ace wrap will probably work best.
Once you notice a lack of drainage or exudate in the bandages, you're ready to remove the dressing and expose to the air. Use your best judgment whether the wound is closed or not. You'll be able to tell best by how it feels when you touch it.
As an orthopedic technician, I do a fair amount of wound care. Follow this regimen, and you should heal rapidly. Everyone heals differently though. But I hope you yield similar results to mine.