CALCULATION OF FULLY-DEVELOPED FLOWS OF COMPLEX FLUIDS IN PIPES OF ARBITRARY SHAPE, USING A MAPPED CIRCULAR DOMAIN

The problem of determination of fully developed duct flows of arbitrar y shape is considered for fluids obeying various constitutive equation s. A numerical method based on the transformation of the physical flow (simply connected) domain into a mapped circular domain is set up. Th e numerical determination of the unknown transformation between the tw o domains leads to knowledge of the velocities and stresses in the duc t, starting from circular contour values of the velocity in the mapped computational domain. Different constitutive equations are investigat ed for several flow geometries. The comparisons with existing analytic al solutions are found to be consistent for all the geometries tested. The method may provide a useful tool for determination, in steady flo w conditions, of the flow characteristics for various types of ducts a nd constitutive equations.