A Experimental and Computational Study of Flow Instability in a Helical Coil.
Abstract
This study concerns the transitional regime between laminar and turbulent flow states in a helically coiled pipe of circular crosssection. 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. LaserDoppler velocimetry (LDV) measurements of two instantaneous velocity components were obtained along the midplane of the pipe crosssection 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 crosssection 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 NavierStokes equations formulated for the toroidal coordinate system. The unsteady threedimensional 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 crosssection and the flow in the crossstream wall layer. The flow perturbation consists of a pair of counterrotating vortices aligned in the crossstream circumferential direction. This suggests that the traveling wave is a result of a centrifugal instability of the crossstream flow.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT.......114W
 Keywords:

 Engineering: Mechanical; Physics: Fluid and Plasma