TY - JOUR
T1 - Secondary instability of flow in a curved duct of square zross-section
AU - Mees, Philip A.J.
AU - Nandakumar, K.
AU - Masliyah, J. H.
PY - 1996/9/25
Y1 - 1996/9/25
N2 - Experiments and simulations of a travelling wave state of incompressible Newtonian flow in a curved duct of square cross-section are presented. The travelling wave mode develops from the well-documented steady four-cell flow state and is characterized by oscillations of the two Dean vortices near the centre of the outer wall. The oscillations were induced by a carefully positioned pin at 5° from the inlet of the curved section along the symmetry line of the cross-section. It was shown that the travelling wave state is characteristic for curved duct flow and that the pin made it possible to observe the oscillations within the 270° long curved duct. Travelling waves were observed at flow rates above Dn = 170 (Dn = Re/(R/a)l/2, where Re is the Reynolds number, R is the radius of curvature of the duct and a is the duct dimension. The curvature ratio, R/a, is 15.1). If no other disturbances are imposed, the oscillations are the result of the selective amplification of random disturbances in the flow, leading to a broad frequency spectrum. The travelling wave was found to lock in to an imposed periodic disturbance at a selected frequency. The flow structure of the locked state was investigated in detail, using flow visualization and a one-component laser Doppler anemometer to measure streamwise or spanwise velocities. Direct numerical simulations using the package CFDS-FLOW3D are in very good agreement with the experiments and confirm the existence of a fully developed, streamwise-periodic travelling wave state. The inflow region between the two Dean vortices, which transports low-speed fluid away from the outer wall, creates strongly inflectional spanwise profiles of the streamwise velocity. Similarities with twisting vortices in a curved channel and sinuous oscillations of Görtler vortices show that the travelling waves observed here result from a secondary shear instability of these spanwise inflectional profiles.
AB - Experiments and simulations of a travelling wave state of incompressible Newtonian flow in a curved duct of square cross-section are presented. The travelling wave mode develops from the well-documented steady four-cell flow state and is characterized by oscillations of the two Dean vortices near the centre of the outer wall. The oscillations were induced by a carefully positioned pin at 5° from the inlet of the curved section along the symmetry line of the cross-section. It was shown that the travelling wave state is characteristic for curved duct flow and that the pin made it possible to observe the oscillations within the 270° long curved duct. Travelling waves were observed at flow rates above Dn = 170 (Dn = Re/(R/a)l/2, where Re is the Reynolds number, R is the radius of curvature of the duct and a is the duct dimension. The curvature ratio, R/a, is 15.1). If no other disturbances are imposed, the oscillations are the result of the selective amplification of random disturbances in the flow, leading to a broad frequency spectrum. The travelling wave was found to lock in to an imposed periodic disturbance at a selected frequency. The flow structure of the locked state was investigated in detail, using flow visualization and a one-component laser Doppler anemometer to measure streamwise or spanwise velocities. Direct numerical simulations using the package CFDS-FLOW3D are in very good agreement with the experiments and confirm the existence of a fully developed, streamwise-periodic travelling wave state. The inflow region between the two Dean vortices, which transports low-speed fluid away from the outer wall, creates strongly inflectional spanwise profiles of the streamwise velocity. Similarities with twisting vortices in a curved channel and sinuous oscillations of Görtler vortices show that the travelling waves observed here result from a secondary shear instability of these spanwise inflectional profiles.
UR - http://www.scopus.com/inward/record.url?scp=0030237177&partnerID=8YFLogxK
U2 - 10.1017/S0022112096000973
DO - 10.1017/S0022112096000973
M3 - 文章
AN - SCOPUS:0030237177
SN - 0022-1120
VL - 323
SP - 387
EP - 409
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -