Investigation on Energy Distribution in Steady and Unsteady Flow Instabilities through a Bend Square Pipe

Fluid flow analysis through a bend pipe is extensively conducted in practical and cell separation operations. It is observed that flow behaviors in the bend pipe are influenced by some parameters such as curvature, aspect ratio, etc. As a result, various phenomena, steady solution branches, unsteady solutions, energy transfer are changed. In this paper, the acts of flows are performed together for fixed curvature, δ = 0.2, and Prandtl number, Pr = 7.0 (water). Here, for a wide variety of Dean numbers (100 ≤ Dn ≤ 1000) and three fixed Grashof numbers, Gr = 100, 500, and 1000; time-independent solutions with linear stabilities are investigated first where only the first steady branch exhibits linear stability out of two steady solution branches obtained. Then, different flow transitions between the required range of Dean numbers (Dn) and several Grashof numbers (Gr) are investigated using time-dependent solutions. Power spectrum density (PSD) is further revealed in order to gain a deeper understanding of periodic and multi-periodic flows. Flow velocity contours including axial flow (AF) and secondary flow (SF) and their temperature profiles (TP) are also exposed. The SFs reveal that two- to four-vortex flows are produced due to the turning of steady branch and the flow instabilities. Furthermore, the energy transfer between the cooled and heated sidewalls of the pipe is calculated. Finally, a link between centrifugal and body force with the energy transfer has been shown in this research which reveals that the fluid has merged that certainly rises the overall energy transfer.