Dean vortex stability using magnetic resonance flow imaging and numerical analysis

Abstract

AbstractMagnetic resonance flow imaging using flow encoding with spin warp imaging was used in three dimensions to measure velocity profiles and the dynamic behavior of centrifugally‐induced (Dean) vortices in curved tube flow. Experimental measurements were compared with numerical simulations obtained from the solution of Navier‐Stokes and continuity equations using a commercial finite‐element package. Effects of flow rate and geometry, and the ratio of the tube radius to that of curvature on the stability of Dean vortices were studied. Twisting and bifurcation of vortices increased with increasing flow rate and radius ratio. A six‐vortex pattern was measured experimentally and predicted numerically. Additional wall shear rates, due to Dean vortices, were estimated from velocity measurements in the cross‐sectional plane. A phase diagram was constructed to establish conditions for the existence of two, four or six vortices as a function of flow rate and curvature. Experimental observations were compared with numerical results obtained from three types of finite‐element grids. The full‐tube grid without symmetry planes was most predictive for vortex bifurcation, while the pseudo‐cylindrical full‐tube grid with a plane of symmetry gave best results for shear rates. Results from the numerical analysis agreed qualitatively well with the MRI measurements.