Developing Flow and Heat Transfer in Strongly Curved Ducts of Rectangular Cross Section

Abstract

A numerical study of heat transfer in 90 deg, constant cross section curved duct, steady, laminar, flow is presented. The work is aimed primarily at characterizing the effects on heat transfer of duct geometry and entrance conditions of velocity and temperature by considering, especially, the role of secondary motions during the developing period of the flow. Calculations are based on fully elliptic forms of the transport equations governing the flow. They are of engineering value and are limited in accuracy only by the degree of computational mesh refinement. A comparison with calculations based on parabolic equations shows how the latter can lead to erroneous results for strongly curved flows. Buoyant effects are excluded from the present study so that, strictly, the results apply to heat transfer flows in the absence of gravitational forces such as arise in spacecraft.

Numerical study of non-isothermal flow with convective heat transfer in a curved rectangular duct

“…In both investigations, temperature and velocity results showed clear evidence of secondary flows. Yee et al [14] conducted numerical calculations to predict steady laminar flows with the boundary conditions of constant temperature in channels with aspect ratios of 0.33, 1 and 3 where no gravitational effect and hence no buoyancy effect was included. Komiyama et at.…”

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

“…Its extension and validation for predicting forced convection heat transfer in curved duct flows may be found in [5]. A brief outline is given here of the adaptation of the calculation scheme in [5] to flows with buoyant effects to which the Boussinesq approximation apply.…”

“…Depending on the relative orientation (with respect to gravity) of a curved duct geometry and the ratio of buoyant to inertial forces, reversed flow regions can be expected to appear in curved duct flows subjected to thermal effects. Examination of the literature published to date suggests that, although forced convection heat transfer has been investigated (see, for example, [5]), thermally induced buoyant motion in developing curved duct flow has peceived comparatively little attention [2,10,11]. 'This ;-s the case in spite of the relativeeasewHh which conditions are attained propitious to the occurrence of the phenomenon.…”

“…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].…”

“…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]~-.…”