Abstract
A numerical study is presented for the fully developed two-dimensional laminar flow of viscous incompressible fluid through a curved square duct for the constant curvature δ = 0.1. In this paper, a spectral-based computational algorithm is employed as the principal tool for the simulations, while a Chebyshev polynomial and collocation method as secondary tools. Numerical calculations are carried out over a wide range of the pressure gradient parameter, the Dean number, 100 ≤ Dn ≤ 3000 for the Grashof number, Gr, ranging from 100 to 2000. The outer wall of the duct is treated heated while the inner wall cooled, the top and bottom walls being adiabatic. The main concern of the present study is to find out the unsteady flow behavior i.e. whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn or Gr is increased. It is found that the unsteady flow is periodic for Dn = 1000 at Gr = 100 and 500 and at Dn = 2000, Gr = 2000 but steady-state otherwise. It is also found that for large values of Dn, for example Dn = 3000, the unsteady flow undergoes in the scenario “periodic→chaotic→periodic”, if Gr is increased. Typical contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of single-, two-, three- and four-vortex solutions. The present study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal force in a curved square passage that stimulates fluid mixing and consequently enhance heat transfer in the fluid.
Highlights
Fluid flow and heat transfer in curved ducts have been studied for a long time because of their fundamental importance in engineering and industrial applications
Time Evolution of the Unsteady Solutions Time evolution of the resistance coefficient λ are performed for Dn = 100 and 100 ≤ Gr ≤ 2000 as shown in the contours for the stream lines of the secondary flow patterns (ψ ) and temperature profiles (T), we use the increments ∆ψ =0.6 and ∆T = 0.25 respectively
Since the flow is steady-state, single contours of the secondary flow patterns and temperature profiles are shown in Figure 2(b), where it is seen that the unsteady flow is an asymmetric single- and two-vortex solution
Summary
Fluid flow and heat transfer in curved ducts have been studied for a long time because of their fundamental importance in engineering and industrial applications. The flows in curved non-circular ducts are of increasing importance in micro-fluidics, where lithographic methods typically produce channels of square or rectangular cross-section. These channels are extensively used in many engineering applications, such as in turbo-machinery, refrigeration, air conditioning systems, heat exchangers, rocket engine, internal combustion engines and blade-to-blade passages in modern gas turbines. Centrifugal forces are developed in the flow due to channel curvature causing a counter rotating vortex motion applied on the axial flow through the channel This creates characteristics spiraling fluid flow in the curved passage known as secondary flow. Many theoretical and experimental investigations have been done; for instance, the articles by Berger et al [2], Nandakumar and Masliyah [3], and Ito [4] may be referenced
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