The widely used boundary condition for in rotating machinery inlet is turbulentMixingLengthDissipationRateInlet. omega:

 boundaryField
 {
".*_inlet"
    {
        type            compressible::turbulentMixingLengthDissipationRateInlet;
        mixingLength    0.1;
        phi             phi;
        k               k;
        value           $internalField;
    }
 }

For internal flows the parameter mixingLength is recommended to be equal to hydrostatic diameter of the pipe.