The profiles are created mathematically.

Have a look on Deich et al. (1965) work. You will get your answer for turbomachinery.

This PDF is avaliable online.

Santosh Kumar Singh yeah but they always use this NACA Profiles or there is other profiles

why not I think so

In the beginning of gas turbine design they sure did use naca profiles, because of the large amount of experimental data that was available for this type of profile.

Other types of profiles are for example double circular arc or controlled diffusion airfoils. Todays blade design is based on numerical methods and optimization is often used to improve the profile performance. These profiles do not follow a standard like the naca profiles. The gas turbine technology is at such a high end level, that every blade is tailored for the specific application, to give maximum performance. This and the fact that blade profiles are a trade secret of the manufacturers, prevents standardization of modern blade profiles.

The NACA profiles are the standards in the industry that is correct although some others are trying to establish some standards but they are significant . There are other profile designs, but they are propriety information and mostly unpatented or available in the public domain.

numerical methods need to be verified experimentally. I'm sure some wind tunnels have the capabilities to perform at the pressures and speeds needed. As the turbine blades are usually small, models can be easily constructed and tested at the corresponding real Re and Mach numbers

As far as I know, NACA profiles are the standards that are used in both industry and research (turbomachines, aerospace, etc). I would say, any new profiles or modifications are also predominantly based on NACA profiles.

Yes, of course. I think you can choose the airfoil with more chamber