What is the significance of mach number, pressure and velocity variation profiles?
I read a lot of papers on spray modeling using different software packages like Kiva, Star CD etc. what's the exact role of this modeling in combustion modeling?
Your question is too general, I can only suggest a reading on basic textbooks of gasdynamics (for example Zucrow). Then, go to to the topic of the combustion (that can happens also at very low-mach)
Mach number is used to compare the flow velocity with local speed of sound, pretty significant in a gas turbine as formation of shockwaves could pose unwanted situation. Pressure plays a very significant role in any combustion, if the pressure before the combustion is high, the work output (expansion) will also increase.
You may measure the pressure and velocity quite independently. But, it is less direct in case of the Mach number. The Mach number depends on the local sound velocity u_a which again depends on the local temperature through u_a=sqrt(gamma R T).