Mixing length model for compressible turbulent flows in rough channels

Compressible turbulent flow in a rough channel, which possesses the character of a developing flow when heat is continuously introduced over the length of the channel, is studied. The velocity and the temperature field, as well as the axial variation of the pressure, the friction factor, and the Stanton number in such a thermally developing flow are calculated. The turbulent contributions to the momentum and the energy transport are determined using a mixing length model. The free parameters occuring in the mixing length model are determined so that the calculations correctly describe the limiting case of a fully developed incompressible flow in a smooth or rough pipe. A correlation between the mixing length of the hypothetical rough wall and the relative sand grain roughness is developed. The effect of compressibility on the friction factor and the Stanton number is examined.