An experimental and computational study of flow instability in a helical coil

This study concerns the transitional regime between laminar and turbulent flow states in a helically coiled pipe of circular cross-section. The study consists of complementary experimental measurements and numerical calculations in a coil with a radius of curvature to pipe radius ratio (R;A new test section and flow apparatus were constructed. The streamwise pressure drop measurements agreed very well with those of previous investigations. Laser-Doppler velocimetry (LDV) measurements of two instantaneous velocity components were obtained along the midplane of the pipe cross-section at a nominally fully developed location in the coil. Thirteen Reynolds numbers were examined in the range 3800 ;The CUTEFLOWS algorithm was modified to solve numerically the finite difference approximation of the Navier-Stokes equations formulated for the toroidal coordinate system. The unsteady three-dimensional calculations were performed for Re = 5480 (De = 1280). The mean characteristics of the flow predicted by the calculations agree very well with the experimental data. The flow perturbation due to the traveling wave agrees qualitatively for all three grid refinements and with the experimental data. The calculated results indicate that energy is transferred to the traveling wave from the mean flow through a complex interaction between the centripetal acceleration in the inner half of the pipe cross-section and the flow in the cross-stream wall layer. The flow perturbation consists of a pair of counter-rotating vortices aligned in the cross-stream circumferential direction. This suggests that the traveling wave is a result of a centrifugal instability of the cross-stream flow.