The secondary ow structure in a helical pipe with large torsion is investigated by using a numerical calculation of a uid particle trajectory and an experiment using a smoke visualization technique. Good agreement is obtained between the experiment and the numerical calculation. The secondary ow in a cross-section is transformed from a two counter-rotating vortices structure to a one-recirculation structure with increase of the torsion of the pipe at a constant Dean number. The line dividing two vortices varies its direction from horizontal to vertical as the torsion increases.

The secondary flow in a curved duct of square cross-section is investigated experimentally using a visualization method. Three walls of the duct (except the outer wall) rotate around the center of curvature and an azimuthal pressure gradient is imposed. Photographs of the flow in a cross-section at 180 • downstream from the curved duct entrance are taken by changing the flux (Dean number) at a constant rotational speed (Taylor number) of the duct walls. Several types of secondary flow are detected. The variation of the flow patterns with change of flow parameters is compared with that of numerical calculations and is found to be in good agreement. The diagram showing types of secondary flow patterns in the Taylor-Dean number plane is obtained.

An objective of the present paper is to experimentally clarify the torsion effect on the flow in helical circular pipes. We have made six helical circular pipes having different pitches and common non-dimensional curvature δ of about 0.1. The torsion parameter β 0 , which is defined by β 0 = τ/(2δ) 1/2 with non-dimensional torsion τ, are taken to be 0.02, 0.45, 0.69, 1.01, 1.38 and 1.89 covering from small to very large pitch. The velocity distributions and the turbulence of the flow are measured using an X-type hot-wire anemometer in the range of the Reynolds number from 200 to 20000. The results obtained are summarized as follows: The mean secondary flow pattern in a cross section of the pipe changes from an ordinary twin-vortex type as is seen in a curved pipe without torsion (toroidal pipe) to a single vortex type after one of the twin-vortex gradually disappears as β 0 increases. The circulation direction of the single vortex is the same as the direction of torsion of the pipe. The mean velocity distribution of the axial flow is similar to that of the toroidal pipe at small β 0 , but changes its shape as β 0 increases, and attains the shape similar to that in a straight circular pipe when β 0 = 1.89. It is also found that the critical Reynolds number, at which the flow shows a marginal behavior to turbulence, decreases as β 0 increases for small β 0 , and then increases after taking a minimum at β 0 ≈ 1.4 as β 0 increases. The minimum of the critical Reynolds number experimentally obtained is about 400 at β 0 ≈ 1.4.

The micromixer, which has a rotor with a curved channel, is studied experimentally. The secondary flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional channel curvature a R   is taken to be about 0.1, where 2a is the width of the channel, R the curvature radius of the channel. Other non-dimensional parameters concerned are the Dean number 1 2 De Re  , the Reynolds number Re h qd   , where q is the mean flow velocity in the channel axis direction, ν the kinematic viscosity, d h the hydraulic diameter of the channel, and the Taylor number     1 2 2 Tr 2 2 a   , wh   ere Ω is the angular velocity of the rotor. Photographs of the flow in a cross-section at 180˚ downstream from the curved channel entrance are taken by changing the flux   De constant rotational speed   Tr the channel walls. It is found that good mixing performance is obtained in the case of at a of De  for that case secondary flows show chaotic behaviors. And then we have confirmed the occurrence of reversal of the mean axial flow. 0.1 Tr and the micromixer of this type is important in a practical use two walls of the channel rotate.

Turbulent flow through helical pipes with circular cross section is numerically investigated comparing with the experimental results obtained by our team. Numerical calculations are carried out for two helical circular pipes having different pitches and the same nondimensional curvature δ (=0.1) over a wide range of the Reynolds number from 3000 to 21,000 for torsion parameter β (=torsion /2δ  = 0.02 and 0.45). We numerically obtained the secondary flow, the axial flow and the intensity of the turbulent kinetic energy by use of three turbulence models incorporated in OpenFOAM. We found that the change to fully developed turbulence is identified by comparing experimental data with the results of numerical simulations using turbulence models. We also found that renormalization group (RNG) k−ε turbulence model can predict excellently the fully developed turbulent flow with comparison to the experimental data. It is found that the momentum transfer due to turbulence dominates the secondary flow pattern of the turbulent helical pipe flow. It is interesting that torsion effect is more remarkable for turbulent flows than laminar flows.