If you have had no basic physics courses, no fluid dynamics/mechanics courses, and no courses in PDEs, you're probably going have a hard time with your application. You might be able to work on things that contribute to solving problems in CFD like linear and non-linear solvers, but your background is lacking when it comes to application for a PhD in an engineering, physics, or mathematics department. You might be better off finding an advisor in a CS program who does interdisciplinary work related to fluids and get in with them. Guys like Ron Fedkiw in CS at UCLA and Martin Berzins at in CS at Utah are Maths PhDs in CS departments working on CFD problems. Working with someone like one of them might give you the time and space to pick up the fluids and PDEs through coursework or reading and working problems while you target some of the more CS-ish problems in their projects.
In the end, it can work out, but I think you'll have a hard time with a frontal assault on an engineering PhD program application. You're going to have to be more targeted in your approach.