what is the use and improtance of dimensionless numbers in cfd

Dimensionless numbers (such as Reynolds Number, Mach Number) are a general concept (extensively used within fluid dynamics) to allow comparison between similar flow physics carried out at different scales and with different fluid properties. For more on the importance of the Reynolds Number try: http://www.symscape.com/node/348

In the cases of Reynolds and Mach numbers the actual values have significance. For example Mach > 1 is termed supersonic flow which has different physical characteristics to Mach < 1 (subsonic flow).

CFD can match the full scale geometry and fluid physics, so dimensionless numbers for scaling are less relevant. However, typically when presenting fluid flow results dimensionless qualities (such as lift and drag coefficients) are quoted. Hence the appearance of reference variables (such as area, pressure and velocity) in many CFD software packages.