# Reynolds Number

Dimensionless lift coefficient and drag coefficient values permit comparisons between similar shapes moving through a fluid. Such comparisons are only valid if the Reynolds numbers are also equivalent.

The Reynolds number indicates which regime a flow follows - laminar, in transition or turbulent. The dimensionless Reynolds number is defined as:

mu . Re = rho . V . L

where:
Re is the dimensionless Reynolds number
rho is the fluid density
V is the free stream fluid speed
L is a characteristic length, for an airfoil it is the chord length
mu is the fluid viscosity

One of the problems when a scaled model is tested in a wind tunnel is that the Reynolds number for the model can be significantly different from that for the real world object. Thus, the model may experience laminar flow and the real-world full-size object may experience turbulent flow. This difference, revealed by the Reynolds numbers, would manifest itself as discrepancies in lift and drag if these dimensionless quantities are extrapolated from the wind tunnel data to their full-size equivalent. This effect is especially pronounced when the airfoil is near its stall condition.

To ensure that the Reynolds numbers are equivalent between scaled models and their full-size counterparts, there are a number of options that can be considered:

• Use as large a model as possible. Thus, the aim is for the characteristic model length (L) to be large enough to produce the same flow regime (e.g., turbulent) as the full-size equivalent. The drawback is that the larger the model the more expensive the wind tunnel needed to accommodate it in order to avoid blockage effects corrupting the data.
• Reduce the model size and use a water tunnel. This reduces the characteristic length (L), reduces the fluid velocity (V), increases the fluid viscosity (mu) and significantly increases the fluid density (rho) relative to air. The drawback is that it may be difficult to incorporate necessary details and instrumentation on such a small model.
• Pressurize the wind tunnel. This increases the fluid density (rho). The drawback is the extra expense to build and operate a pressurized wind tunnel.
• Increase the wind tunnel speed. This increases the fluid speed (V). The drawback is that the experiment may exhibit supersonic flow regions, thus corrupting the data if the full-size equivalent flow is fully subsonic. Also the higher the wind tunnel speed the more costly it is to construct.

One of the advantages of Computational Fluid Dynamics (CFD) is the ability to run simulations at full size, thus exactly matching the full-size Reynolds number.