Secondary flows in pipes of square cross-section and the measurement of the second normal stress difference
Journal of Non-Newtonian Fluid Mechanics, 1 (2):
107--123 (April 1976)DOI: 10.1016/0377-0257(76)80011-0
Abstract
In this paper, we are concerned with the possibility of determining the second normal stress difference v2 for elastic liquids from a study of the direction and strength of the secondary flows in pipes of non-circular cross-section. Experimental results show that the direction of the secondary flows in pipes of square cross-section is the same for six different elastico-viscous systems, although there is some evidence to suggest that the sign of v2 may not be the same for all the test liquids. The situation is clarified by a theoretical analysis which involves the numerical solution of coupled partial differential equations. From the analysis, it is concluded unequivocally that the direction of the streamlines is no indication of the sign of v2.