Wall-modeling in LES is of high importance to allow the scale-resolving simulation of industrial-scale applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on the Reichardt formula. This work presents a new scaling of this formula to properly take the compressibility effects into account. This new wall-model is validated against wall-resolved-LES on three adiabatic turbulent channel flow cases at moderate Reynolds number, with increasing Mach number and up to M=1.5. The proposed wall-model is then applied to turbulent channel flow cases at high Reynolds number in the quasi-incompressible and supersonic regimes. Finally, the wmLES of a supersonic air ejector is performed and the results are compared to those obtained with RANS simulations.