Thermal flow in ducts and application of a new numerical method for the study of the incompressible laminar flow in curved and helical ducts

A new computational method is presented for the study of general three-dimensional parabolic or partially parabolic incompressible flows. The method is based in the use of a co-location grid for the velocity components and the pressure field, the insertion of three additional variational representations for the continuity, the vorticity and the pressure equations respectively and is named, in short, as CVP computational method. The method is used for the study of the characteristics of the laminar incompressible flow in a square cavity with a moving boundary, for the study of fully developed flow and heat transfer in curved square ducts and for the study of fully developed flow in helical square ducts. Also, results are presented for the problems of the thermally developed flow in straight elliptic or square finned ducts. Numerical results are presented for the effects of the flow parameters like the curvature, the torsion, the Dean number, the Prandtl number and the stream pressure gradient on the velocity, the temperature, the friction factor and the Nusselt number distribution. The new CVP method does not introduce the spurious pressure field oscillations presented in other pressure-linked methods. The use of co-location grid yields to an ease discretization of the involved equations, reducing the mathematical complexity, particularly in the case of complex geometries. The validity and the accuracy of the method is discussed and the results are in close agreement with those obtained by other methods. For the case of the flow in a helical square duct, the results show that the torsion deforms substantially the symmetry of the two vortices of the secondary flow. The friction factor decreases for torsion in the range 0 to 0.1 and increases as the torsion increases further, a behaviour which is more profound as the Dean number increases. Our results are stable for the calculated Dean numbers