What is the normal acceleration of a particle in projectile free fall?

gravity on earth is 9.81N so acceleration would be 9.81 m/s^2

I hate to sound like a politician but...
it depends on what UR definition of "normal" is.

U are correct in that once air friction or drag is ignored, eliminated, or inconsequential,
the only force (ie acceleration) is due to that of gravity.   but this is not normal in the
sense that air friction DOES exist and it is NORMAL to any real situation.

Also, even in 1st year physics the air friction may be given as a constant value, so that it represents another force or acceleration to take into account in the solution of the problem.

There are even "projectile problems" that involve rockets or some other self-propelled
objects, these will have a propulsion force that must be accounted for.

In this level of physics it is normal to ignore air friction etc. However, it must never be forgotten that acceleration is a vector quantity. This is particularly important in projectile problems where you have an object miving upwards and downwards in the same problem. Therefore it is very important to be correct with the definition of acceleration of such an object:
The acceleration of an object in free fall is always 9.81m/s² downwards.