The Liebeck airfoils are not practical. If you find and read his original papers you will quickly see why. First the optimisation method that be uses imposes a single design point so the airfoil is optimised for one flight condition. Second, and more importantly, the high lift is achieved by designing a section with the shortest possible pressure recovery region on the upper surface and this implies that the boundary layer is on the verge of separation over the entire length of the pressure recovery. A small disturance can thus cause the sudden separation of the flow as opposed to a more progressive separation on a more conservative design. This behaviour was quickly discovered when these sections were used on the wings of racing cars .... at critical points turbulence or cross flows would cause sudden separation, instant loss of dowforce and a spin into the wall. Yes the airfoils produce the high CLs claimed in a wind tunnel, but their performance is too unpredictable to be of practical use.
There are later papers in which attemps are made to design airfoils that are optimised for mutliple design points, which are generally more practical ....
