A 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_{rm c}/a) equal to 18.2. 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 < Re < 10500 (890 < De < 2460) which spans the laminar, transitional, and turbulent flow regimes. In the range 5060 < Re < 6330 (1190 < De < 1480), the time records of the velocity components revealed periodic flow oscillations (at St = 0.25 and 0.5) in the inner half of the pipe cross-section due to a traveling wave instability. Similar low frequency unsteadiness was not observed near the outer wall. A significant local maximum in the rms velocity was observed near the pipe center for Re > 5060 and is attributed to the velocity perturbation of the traveling wave instability. Still photographs and video images of the flow visualization by means of a dye streak in the range 5060 < Re < 6330 (1190 < De < 1480) were analyzed to estimate the wavelength and wave speed of the traveling wave. The rms velocity increases rapidly with Re in the range 6330 < Re < 7590 (1480 < De < 1780) indicating that the flow is turbulent beyond this range. 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.