Curved ducts

As mentioned earlier, in curved channels a secondary flow pattern of two counter-rotating vortices is formed. Similarly to the situation depicted in Figrue 2.43, these vortices redistribute fluid volumes in a plane perpendicular to the main flow direction. Such a transversal mass transfer reduces the dispersion, a fact reflected in the dependence in Eq. (108) at large Dean numbers. For small Dean numbers, the secondary flow is negligible, and the dispersion in curved ducts equals the Taylor-Aris dispersion of straight ducts. 

The most prominent characteristic of flow in curved ducts and helicoidal pipes is the secondary flow induced by centrifugal force due to the curvature of the pipe. Consequently, the friction factor is higher in curved pipes than that in straight pipes for the same Reynolds number. The pitch of the helicoidal pipe also has an effect on the flow. As a result, the heat trans-... 

Spiral coils are curved ducts with varying curvature. The friction factor and heat transfer rate for spiral coils are also included in this section. In addition to the dimensionless parameters used in straight pipes, the following parameters are particularly useful in the case of curved ducts or helicoidal pipes the Dean number De the helical number He, and the effective radius of curvature Rc. These are defined as follows ... 

In this section, emphasis will be given to the correlations used for calculating the friction factors and Nusselt numbers for laminar and turbulent flows in curved ducts, helicoidal pipes, and spiral ducts. These will be presented as the ratio of the friction factor in curved ducts to the friction factor in straight ducts fcJfs and the ratio of the Nusselt number in curved ducts to the Nusselt number in straight ducts Nuf/Nus, in most cases. The subscript c represents curved ducts or helicoidal pipes, while the subscript s denotes straight pipes of the same shape. 

Laminar Flow in Curved Ducts With Elliptic Cross Sections... 

R. K. Shah, and S. D. Joshi, Convective Heat Transfer in Curved Ducts, Handbook of Single Phase Convective Heat Transfer, eds. S. Kaka< , R. K. Shah, and W. Aung, Wiley Interscience, John Wiley Sons, New York, 1987. 

Z. F. Dong, and M. A. Ebadian, Thermal Developing Flow in a Curved Duct of Elliptic Cross Section, Numer. Heat Transfer, part A, (24) 197-212,1993. 

BDn inertial term constant for a curved duct flow, dimensionless Bv formation volume factor, dimensionless... 

The curvature of the duct can be shown to be negligible since a < R, and no secondary flow is induced, thus the curve duct can be treated as straight. Pressure gradients arise from two sources in the duct (1) presence of the utricle and (2) from the cupula. The cupula, when deflected, exerts a restoring force on the endolymph. The cupula can be modeled as a membrane with a linear pressure-volume modulus K = Ap/AV, where Ap is the pressure difference across the cupula, which is produced by a volumetric displacement A V, where... 

Wang, L., Yang, T. Multiplicity and stability of convection in curved ducts review and progress, Adv. Heat Transfer 38, (2004) 203-254. 

Taylor, A. M. K. P., J. H. Whitelaw and M. Yianneskis, Curved Ducts with Strong Secondary Motion Velocity Measurements of Developing Laminar and Tur-bulent Flow, Trans ASME J. Fluids Engg., 104, 350-359 (1982). 

Whenever possible, tendons are assembled in the factory. The wires are first measured off to the required length on a fully automatic cutting bench. Then the bundle of wires is passed through a template and the one anchor head, and button-heads are cold-upset onto the wires at this end. In order to make all the wires parallel, the tendon is then pulled through the template by pulling the anchor head. To keep the differences in the lengths of the wires in a curved duct to a minimum, and to preserve the parallelism of the wires even when they are wound onto reels for transport, the tendon is given three to five complete twists and then bound at intervals of approximately 3 m (approx. 10 ft). Once the tendons are reeled the factory work is finished. 

There is evidence [74—77] that gas-dynamic processes behind the pressure perturbation penetrating into curved ducts or reflecting from non-planar end elements affect explosion phenomena. For these observations some highly reactive stoichiometric mixtures (characteristic time of their chemical reactions and the reaction zones are much less than for gas-dynamic processes) have been used. It reduces the complete pattern of probable interaction regimes and does not allow... 

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