Laminar Incompressible Viscous Flow in Curved Ducts of Regular Cross-Sections

Abstract

The laminar three-dimensional flow in curved ducts has been analyzed for an incompressible viscous fluid. The mathematical model is formulated using three-dimensional parabolized Navier-Stokes equations. The equations are generalized using two indices which permit the choice of Cartesian or cylindrical coordinate systems and straight or curved ducts. The solutions are obtained numerically using an ADI method for a number of duct geometries and flow parameters. The study presents detailed results for developing laminar flow in rectangular curved ducts; also, the effect of longitudinal curvature on secondary flow is fully analyzed. An investigation is made of the occurrence of Dean’s instability and, for curved square ducts, it is found to first appear at Dean number ≃ 143.

Optical sectioning for microfluidics: secondary flow and mixing in a meandering microchannel

“…Since its first demonstration, 11 the secondary flow inside a curved channel [12][13][14][15][16][17][18] has received much attention because it is found in many areas from heat exchangers to human arterial systems. 19,20 All previous experimental works were done with large pipes and utilized laser Doppler anemometry 21,22 or tracers, 11,19,20,23,24 like dye, hydrogen bubble, or powder, to explore the secondary flow.…”

On the finite Dean problem: linear theory

“…This and other aspects of the nonlinear problem are discussed in detail in Kachoyan [28]. [21] where On the finite Dean problem: linear theory p + j odd; p + j even, p + j odd; and all other quantities are as given by Kachoyan [29] with a = 0.…”

“…This type of flow is intended to model flow in curved rectangular pipes, and flow in helically coiled ducts with small pitch. Recent numerical and experimental work on this problem has been carried out by, for example, Winters [38], Hille et al [25], Joseph et al [27], Ghia and Sokhey [21], De Vriend [18] and Cheng et al [13].…”

Numerical computation of buoyancy-induced recirculation in curved square duct laminar flow

“…A review of experimental, analytical and numerical studies up to 1975 is given in [1]. Examples of analytical and numerical· studies for the laminar floW regime are'given ;n, [2][3][4][5][6], ,and for the turbulent flow regime (using two-equation turbulence models) i,n [7][8][9]. While the laminar flow cases have yielded to numerical prediction and are currently limited mainly by cost considerations dictated by computational time and storage requirements, calculations of corresponding Motions driven by buoyant forces arise ducts with curvature the criterion is given turbulent flows are less accurate [9].…”

“…Given the considerable difficulties associated with making measurements, it is surprising to find that no attempt has been made (to the authors' knowledge) to investigate numerically the influence of buoyant effects on the motion and heat transfer in developing curved duct flows. In principle, the accuracy of such computations in the laminar flow regime for an incompressible fluid are limited only by the nature of the equations solved (parabolic, semi-elliptic or elliptic)l and the error incurred lFor flows in ducts of mild curvature wherein longitudinal and cross-stream pressure variation can be decoupled, calculation schemes based on parabolic forms of transport equations [6] (boundary layer equations) may be used. For stronger curvature it is necessary to account more exactly for ellipticity in the pressure field [12], or resort to semi-elliptic or fully elliptic calculation schemes which allow for the direct determination of pressure [3][4][5]8, 9]~-.…”