A criterion for detection of the onset of Dean instability in Newtonian fluids

Forced Convective Heat Transfer and Fluid Flow Characteristics in Curved Ducts

“…The wall heat flux radically changed the flow patterns and showed a tendency to suppress Dean vortex formation. Subsequently, Yanase [12] and Fellouah et al [13,14] confirmed and validated the findings by Chandratilleke et al [11].…”

“…In spite of the perceived benefits in computation, this approach cannot be rationalised because the radial gradient of axial velocity is remotely linked with vortex generation. This short fall is reflected when the model of Fellouah et al [13] failed to detect Dean Instability that was clearly observed in some reported cases [10,11]. With improved capabilities, Chandratilleke et al [20,21] have suggested other approaches that will be discussed later.…”

“…This approach has not been attempted in previous studies [11][12][13][18][19] wherein it was argued that a mesh size less than 1 mm would not improve the accuracy, but only increase the computational time. The mesh refinement of the present analysis clearly identifies that a finer mesh near the wall is critical for detecting the onset of Dean vortices as accurately as possible.…”

“…Fellouah et al [13,14] also have presented a useful three-dimensional model for rectangular curved ducts of aspect ratio within 0.5  Ar  12 and curvature ratio at 5.5    20 and. Considering both water and air as working fluids, their results were was experimentally validated using a semi-circular duct.…”

“…Whilst that approach is adequate for two-dimensional cases, it is not applicable for three-dimensional flow. The work of Fellouah et al [13] used the radial gradient of the axial velocity as a measure of identifying the flow instability. Such technique is not justifiable because the axial velocity change in radial direction is not physically connected with the secondary vortex generation.…”