UFR 4-04 Description
Flow in a curved rectangular duct - non rotating
Underlying Flow Regime 4-04 © copyright ERCOFTAC 2004
This document focuses on the underlying flow regime (UFR) of flow in a rectangular-section curved duct. This flow regime is of particular interest from the point of view of CFD code validation, as it provides a demanding test of turbulence models.
CFD codes have become increasingly important for the analysis and design of fluids engineering systems and products. The validation of such codes for turbulent flows relies on comparisons with carefully conducted experiments which highlight some particular fluid flow phenomenon or influence, the central uncertainty being the fidelity of the turbulence model employed in the code.
Among the factors that have defied accurate representation in CFD codes are the influence of streamwise surface and/or streamline curvature, and the development and decay of secondary motion, by either the Reynolds stresses or cross-stream pressure gradients associated with curvature.
Developing flow in curved ducts of “large” aspect ratio has been measured to study the effect of convex or concave curvature on a nominally two-dimensional turbulent boundary layer. These studies in two-dimensional boundary layers indicate that convex curvature has a stabilising influence (reduces turbulent transport) whereas concave curvature has a destabilising effect (increases the turbulence). The differences between the two are not equal and opposite, however, and no turbulence model has yet succeeded in representing the effect of curvature with precision.
Fully-developed flow in a curved duct of square cross-section exhibits secondary motions, due to curvature-induced pressure gradients, which drive low-momentum fluid from the outer (concave) wall on to the inner (convex) wall. Strong and prolonged curvature leads to the formation of longitudinal vortices on the convex wall. The principal difference between developing (boundary layer) and fully-developed flow is that, in the former, the secondary motion is weaker and confined to the boundary layers. The effects of surface curvature on turbulence are present in these flows as well, but those of the secondary motion generally mask them. Also, the stress-driven secondary motion that is present in any straight upstream segment of the duct interacts with the much stronger pressure-driven secondary motion in the curved section, resulting in a flow that is influenced by many factors. Because of these complexities, square-duct experiments have been used in CFD code validation to test not only the numerical capabilities but also to investigate the performance of turbulence models.
Review of UFR studies and choice of test case
Curved ducts of various lengths and aspect ratios have been employed in the past to study the streamwise curvature effects and secondary motions. A review of the literature indicates two types of experiments. In one, developing flow in curved ducts of “large” aspect ratio has been measured to study the effect of convex or concave curvature on a nominally two-dimensional turbulent boundary layer. Among experiments of this type are those of Smits et al. (1979), Gillis and Johnston (1983), Hoffman et al. (1985), and Muck et al. (1985).
The second type of experiments have been conducted mostly in ducts of square cross section, with short or long straight sections upstream of the curved portion, to study the evolution of the secondary motion in developing and fully-developed flows. Representative experiments of this type are those of Humphrey et al, (1981), Chang et al. (1983), and Iacovides et al. (1990).
The study by Chang et al. (1983), which considers flow in a 180-degree bend of square cross-section, is included in the ERCOFTAC database. It has been used for CFD code comparisons, e.g. Choi et al. (1989).
Developing boundary-layer flow in curved rectangular ducts of moderate aspect ratio has not been studied in the same level of detail as that in square ducts. Patel (1969) made some preliminary measurements in such a flow during the course of a study on curvature effects in nominally two-dimensional turbulent boundary layers.
However, the experimental work on which the present UFR is based is a later experimental study, conducted by Kim and Patel (1994). This provides highly detailed and accurate data, suitable for the validation of CFD codes. It is included as Case C62 in the ERCOFTAC “Classic Collection” database, and has been the subject of several CFD code comparison exercises.
© copyright ERCOFTAC 2004
Contributors: Lewis Davenport - Rolls-Royce Marine Power, Engineering & Technology Division