Cross-Velocity Behavior in Parallel Channel Flow

Exponential decay is found for cross flow velocities superimposed on steady, fully developed axial flows. Experimental data show that this type of flow may occur in the annular gap between fixed concentric cylinders. Here, a circumferential velocity, or cross flow, can exist in the presence of a steady axial flow, where a constant pressure difference is maintained between the ends of the cylinders. This flow field is investigated analytically by approximating the cylindrical surfaces by a pair of parallel walls, where the radii of the two cylinders are assumed to be much larger than the annular gap. Solutions to the Navier-Stokes equations are found for uniformly injected (axisymmetric) cross velocity profiles superimposed on parabolic axial velocity profiles. An approximate matrix method is used to formulate solutions for initially arbitrary cross velocity profiles. Results of the calculations show that the exponential decay of the cross flow becomes increasingly stronger as the axial flow rate is diminished. Experimental data obtained from the cylindrical flow model supported these predictions.