The development of laminar flow in a 180° section of a curved square duct (R/d = 6.45) was studied by laser-Doppler anemometry (LDA). The streamwise flow-velocity component Vϕ and the secondary flow component Vr were measured as a function of Dean number and of the azimuthal angle ϕ. The development of the streamwise flow component was found to be connected with a strong momentum transfer towards the outer wall between ϕ = 0° and ϕ = 60°, with a partial back-transfer of the momentum towards the duct centre (ϕ = 45°–108°), and with little further change of the momentum between ϕ = 108° and 180° near the outer wall. The measurements of the Vr component showed at least one vortex pair in the secondary flow. A second vortex pair with opposing sense of circulation was found to develop near the outer wall only for Dean numbers between 150 and 300, in agreement with numerical calculations. This second vortex pair was found in the region between ϕ = 108 and 171°. Between ϕ = 60 and 108° it was not possible to identify the second vortex pair in the developing flow. However, developing laminar-flow numerical calculations by Humphrey (1982) show that it also arises for K = 485 in a 180° square duct with R/d = 3.35 and Re = 890, and it is a function of inlet flow conditions. From the measured stream-function maximum of the second vortex pair it may be deduced that a curved duct with 180° (20 hydraulic diameters) bend angle is not sufficient to reach fully developed flow conditions at d/R = 1/6.45 and K = 226.

The development and structure of primary and secondary flow in a curved square duct

A laminar, three-dimensional, steady-state model has been solved to determine the nature and effect of thermally driven secondary flows in, a horizontal channel with heated top and bottom surfaces and insulated side walls. The secondary flow is characterized by ascending and descending thermals that form longitudinal vortex rolls and enhance the bottom surface heat transfer and channel friction factor by as much as 400 and 30%, respectively. Parametric calculations have been performed to determine the effect on hydrodynamic and thermal conditions of Reynolds number (100 ≤ Re ≤. 1000), Grashof number (2.5 × 105 ≤ Gr∗ ≤ 6.5 × 104), Prandtl number (Pr = 6.5 and 0.7), top-to-bottom surface heat flux ratio (−1.0 ≤ q1/qb ≤ 5.0), aspect ratio (1 ≤ A ≤ 10), and entrance velocity profile. Conditions near the bottom surface are characterized by mixed convection and are unaffected by heating at the top surface. Conversely, conditions at the top surface are dominated by forced convection and are unaffected by heating...

Numerical simulation of laminar mixed convection in the entrance region of horizontal rectangular ducts

This investigation considers the effects of free convection on the laminar flow of water through a circular duct having essentially constant wall heat transfer rate per unit length of the duct and circumferentially uniform wall temperature. The effect of the Reynolds and Rayleigh number variations on heat transfer results has been analysed for both horizontal and inclined pipe. The experiment has covered the range of the inlet Reynolds number from 200 to 2300, and of the Rayleigh number from 6,000 to 70,000. The effect of pipe inclination has been investigated for slope angle values up to 60°, with laminar ascending flow.

Experimental investigation of combined forced and free convection in horizontal and inclined tubes

Ou Jenn-Wuu

Papers

Natural convection effects on graetz problem in horizontal rectangular channels with uniform wall temperature for large Pr

Combined free and forced laminar convection in inclined rectangular channels

Graetz problem in curved rectangular channels with convective boundary condition-the effect of secondary flow on liquid solidification-free zone

Joule-Thomson effects on thermal entrance region heat transfer in pipes with uniform wall temperature