How would you adjust C_l airfoil values for different Reynolds numbers?

I have graph of C_l (airfoil lift coefficient) as a function of AoA, for Mach 0.7 and Re = 6x10^6.

For a given value of C_l, what would be a good way to estimate that value at a different Reynolds number. 6 million is quite low, most transport jets fly at significantly higher Reynolds numbers.

• Normally, the Reynolds number affects lift very little, except near maximum lift. Could it be you want to ask about drag instead? Sep 3, 2021 at 20:58
• @PeterKämpf I'm looking to adjust C_lmax values precisely. Sep 3, 2021 at 21:48

The following two pictures taken from the classical NACA's “Summary of airfoil data” by Abbott, Von Doenhoff and Stivers depict the trend of $$C_l$$ and $$C_d$$ in respect of $$Re$$:

Reynolds number is defined as the ratio of the inertial force possesses by the airflow in relation to the viscous (shear) forces within it:

$$Re=\frac{\rho Vc}{\mu}$$

This can be better seen multiplying both numerator and denominator by $$V$$ and rewriting the definition of $$Re$$ as:

$$Re=\frac{\rho V^2}{\mu(V/c)}$$

Now the numerator resembles the classical expression for kinetic energy while the denominator represent the shear force given by the viscosity $$\mu$$ due to a speed variation $$V/c$$.

So, big Reynolds numbers imply bigger inertial forces than viscous ones. Small Reynolds numbers imply bigger viscous forces than inertial ones.

Intuitively that means that at small Reynolds numbers, viscous characteristics are predominant: thicker boundary layer, bigger viscous drag and earlier stall i.e. lower $$C_{l_{max}}$$.