Numerical Calculation of the Laminar Inlet Flow. I

Abstract

The velocity profiles of the boundary layer in the laminar inlet flow are calculated numerically. The boundary layer equation is simplified assuming similarity of the velocity profiles in a weak sense and this equation is integrated numerically at various cross-sections corresponding to δ=0, 0.01, ···, 0.16, where δ denotes the displacement thickness. The calculation is not extended beyond δ=0.16 since the inviscid core disappears at this point. The relation of δ with the axial distance z is obtained from the continuity of flux, and thus the profiles of the axial velocity u at various cross-sections are obtained as functions of the radial distance r. Finally the error due to the assumption of weak similarity is estimated.