Pressure drop coefficient of laminar Newtonian flow in axisymmetric sudden expansions

Abstract

Laminar flow of a Newtonian fluid in an axisymmetric pipe expansion has been studied numerically by means of the finite-volume approach. Predicted values of some of the overall flow characteristics, such as recirculation length, its strength, and centre location, were compared with available experimental data and correlations, and good agreement was found. The purpose of the work was to evaluate the pressure-loss coefficient Cl for a range of Reynolds numbers and to compare the results with existing simplified theory, which is based on a one-dimensional (1-D) overall balance of energy and momentum. Considerable differences were found, which lead us to formulate corrected theoretical equations in the scope of the 1-D approximation. These corrections were evaluated from the numerical results and accounted for three effects: (1) differing actual and fully developed wall friction; (2) distortion of velocity profiles from the parabolic shape at the sudden expansion section; and (3) nonuniformity of pressure at the expansion plane. Predicted values of the loss coefficient agreed to within 4% with the corrected theory and were found to be proportional to the inverse of the Reynolds number for Re ≤ 17.5 [with effect (3) above predominant and accounting for up to 85% of Cl] and approximately constant for Re > 17.5 [with effect (1) above predominant and accounting for 20% of Cl]. Finally, a correlation for calculating the local loss coefficient as a function of the Reynolds number for the 1:2.6 sudden expansion and fully developed conditions is proposed.